Arrow - S8 E3 - Leap of Faith

Are you talking about Bruce and Barbra sleeping together?  Because I'm pretty sure that's never actually happened in the comics.  The only instance I'm aware of is in The Killing Joke animated movie; and a relationship between them hinted at in Batman Beyond, which sort if and sort of isn't part of the same continuity as The Killing Joke, since most of the same people were involved with both, but what is or isn't cannon between them isn't clear.  But yeah, I couldn't find any indication that this ever happened in the comics; and that's actually a point of contention among fans of the comics that they included it in the movie.
Frankly, I'm terribly bothered by the idea of Bruce and Barbra hooking up under certain circumstances; though her being "barely legal" wouldn't be one of them.  I think a scenario where Barbara was distinctly an adult and the two had been working alongside each other closely for years would make it plausible.  I've even considered this as a possible catalyst for Dick and Bruce's estrangement if it happened while Dick was still relatively young (17-19), clearly had an infatuation with Barbara that had not yet been returned; Bruce was oblivious to Dick having a crush on Barbara, Babs may or may not have perceived it herself, or at least had not openly acknowledged it.  So when it happens and Dick finds out, maybe sees something without the other two knowing, it hurts Dick.  Meanwhile, in the case of Bruce and Barbara, I'd see it as something that might happen between them in the heat of the moment, following a tense engagement with someone, but you know, not on the roof somewhere; after they've returned to the cave and take things upstairs.  But then the next morning, in the harsh light of day, they evaluate how this should change their relationship, or if it should change their relationship; and it could be Barbara that decides she doesn't see her and Bruce dating, she doesn't want to date him.  She might even bring up not wanting to hurt Dick, acknowledging his crush for the first time and cluing Bruce in on it; which of course makes him feel like a dick.  They don't try to bury it and pretend like it never happened though; they accept that it did, that there was a moment where they gave into.....something.... call it the moment, call it passion or a need to share something intimate with another person.  And maybe if they ever feel that need again, it could happen again, but neither are seeking a deeper emotional investment for the other.  Unlike Bruce and Dick's relationship, Bruce isn't a surrogate father for Barbara, and she's not his ward or daughter.  She may happen to be the actual daughter of a close friend of his, but that doesn't change the sort of relationship she and Bruce cultivate as masked crime fighters.  Her father may be his friend - as close of friend as one can be, without revealing who you really are - but Bruce is her friend too; and I think it would make sense for Bruce to eventually see her in that light, as an adult and as a peer.

I mean, to start with, in a comparison of Bruce vs. Ollie, Olive Queen on Arrow has definitely killed people; whereas I'm not aware of that being true at all for Batman in the Arrowverse.  That was definitely a point of contention for people with the DCEU; the ambiguity of Batman's position of lethal force with the Nolan trilogy was one of the things I never cared about that.  The cavalier way some of the characters on Titans killed people was one of the things I definitely didn't like about that show, having just finished the first season.

This is a concept about Batman that I've never cared for, and always ends up being the defining trait when depicting him in movies or any other form of adaptation; and has even seeped into the comics in recent year (okay, the last decade or two) and arguably that just shouldn't be the case.  A Batman who is not, to some degree, well adjusted, who just beats up on people and uses those closest to him as nothing more than cannon-fodder, is not a hero; he's the sort of person who deserves to be in Arkham alongside all of the other dangerous psychopaths. 
It drove me crazy watching Titans every time Dick groused about Bruce just using him or Jason (or Jason's comment about Bruce making the Robin costume bright and colorful to intentionally draw the bad guy's fire, so Batman can get the upper hand.)

This is not who Batman should be.  And it didn't used to be.  There needs to be nuance to this character.  He's supposed to be the greatest detective in the world; he is supposed to be, arguably, a genius who has not only mastered an untold number of fighting styles and honed his body to the height of human aspiration, but has also developed his mental prowess to equal levels.  He's studied meditation, forensic science, chemistry, presumably he's learned some hardcore computer program and engineering, that he's able to create his wonderful toys without the need of involving too many people from outside.
One of the best takes I've read on Batman wasn't even a comic, it was novel called "The Forensic Files of Batman"; and it was written in the style of being Bruce's case file and sometimes his personal journals, dating back to childhood, and at least one entry from Alfred, pertaining to a case he was more involved in.  And it explored those nuances that usually get glossed over in the conventional Batman stories; like the idea that Bruce is actually very methodical about how he investigates an active crime scene, making sure not disturb it in such a way that could influence the police department's own investigation.  He takes samples of evidence, making sure the police have their own evidence to still collect; his gloves are designed to allow for the sensitivity and tactile grip to be able to pick things up as though he weren't wearing gloves, but thick enough not to leave prints.  And he has all this forensic analysis equipment in the Batcave.  I'm fairly certain this book also featured a story from Bruce's youth that had Alfred giving him a children's chemistry set or forensic set, as something to try and raise his spirits in the months after his parents death; which then piqued his interest in science.

While I realize this isn't strictly in-line with what's been depicted of the character, even in the comics, and is far more in the camp of "fan theory," I've always thought they put the horse ahead of the cart in Bruce's reason for his training or for becoming Batman.  He spends all this time away from Gotham to train - years, ostensibly decades in the comics - in effect in order to become Batman, without knowing he's going to be specifically Batman, all solely out of emotional damage of his parent's brutal murders.
But I would argue that for all of the time and training Bruce would have to put in, that it would be difficult, if not impossible, for Bruce not to come to terms with his parents death and become more well adjusted; and that he would need a better motivation to become Batman.  As I see it, his parents death makes sense as the catalyst for the start of his journey, but not the be all, end all of it.  If I were writing his story (which I fully admit, I'm not, but I'm going to share the idea with you anyway) to help Bruce cope with his parent's death and being afraid that their killer will come back for him, Alfred enrolls him self-defense training, which takes well to; and keeps wanting to learn more and continues to advance.  To ensure he doesn't just focus on the physical elements, on fighting or protecting himself, Alfred gets him interested in science and in computers, robotics.  Bruce's thirst for knowledge becomes insatiable and he begins to look outside of Gotham for the next skill to master or fact to learn - but he doesn't want the world to know.  He's tired of being in the spotlight for the rich boy who lost his parents, so he often finds ways of taking these trips beyond Gotham under false identities and eventually begins to leave false trails in order to lead the paparazzi on a wild goose chase; something he comes to take a certain level of perverse pleasure in.  He's never fully out of public view; he doesn't go missing or anything, but he does come back to Gotham less and less and for shorter and shorter intervals.  While he's gone he learns mental disciplines and meets people who help him come to peace with the original reason he's started this journey, which allows him to master certain disciplines he ostensibly couldn't if he held onto that emotional baggage, but his innate curiosity continues to drive him.  
When all is said and done, Bruce manages to come through the death of his parents healthy, happy and well adjusted; and it's only when he eventually returns to Gotham and discovers how much has changed under his nose and during his prolonged absences, that he decides to put his cultivated talents to use to make a difference.  He doesn't realize at first the quagmire he's entering into though; he identifies one underlying problem, then another and another - and therein lies the true nature of the story of Bruce Wayne/Batman; it's a tragedy.  Not because his parents die, but because Bruce managed to survive their death and would have lived a happier life had he never returned to Gotham. And by doing so, he just keeps getting sucked in to the next disaster, the next crisis, the next villain; it keeps demanding more from Bruce and he keeps trying to shoulder the burden, until finally, eventually the job will kill him.