There's a few things going on in the dinner scene where Dent first meets Bruce in person, notably the fact that Bruce appears to be going out of his way to impress Dent's date, Rachel. He's evidently arranged a 'coincidental' meeting at a restaurant (that he just happens to own - Rachel even accuses him of having bought it only a few weeks ago in the novelisation) and bringing a floozy along with him (a world famous ballerina, no less, who'll be headlining the ballet performance that Dent is taking Rachel to later that week), presumably to make her jealous. Harvey is simultaneously threatened by Bruce's long-standing friendship with Rachel, suspicious that Bruce is actually trying to woo her and (even if he's not), intimidated that Bruce may have gone to the time, effort and expense of buying an entire restaurant just to screw with her.
Obviously we know that Bruce is actually there to try to size up Dent as a person, to determine whether he's crooked before deciding to support him financially and to gauge whether to throw his, not inconsiderable resources behind his campaign to clean up Gotham.
In short, Bruce is going out of his way to be Bruce Wayne, noted dilettante & playboy when in reality, he's there to see whether Dent is a potential ally in his war on crime. Alienating Dent (a little) is actually part of his plan.