When Bruce recognizes Ra's Al Ghul is back, he realizes he needs to end the party and get rid of everyone.
Bruce Wayne actually wanted everyone to leave before he even joined the party, just after asking Alfred if Fox was still there. With Bruce having just brought in Rachel [who had been poisoned], and with Fox being there, Bruce was more concerned with being Batman than he was maintaining the Wayne name and image. This is the argument that he and Alfred have just before Bruce joins the party.
What was the point of this? Was it because he was drunk?
No, he wasn't drunk, though he did play the part of one so that he could be perceived as a drunken jerk, thus allowing him to speak so rudely. Bruce wanted everyone to leave immediately, and so, throwing out insults and directly telling them to leave (and that it's not a joke), was his strategy.
Or was it because he genuinely does not like these people and do not want them to return?
This is much more likely the case. First off, the party was to celebrate Bruce Wayne's birthday, and Bruce doesn't like attending parties (most especially those where he's the spotlight, unless it serves another purpose/he has an "agenda"). Secondly, Bruce just doesn't like the rich and powerful of Gotham. Generally speaking, he finds them fake and pompous.
I mean by doing this he ruined the Wayne name as one person even said "The apple really has fallen far from the tree Mr. Wayne".
For Bruce, although his comments did significantly tarnish the Wayne name (i.e., his father's name), once he found out that Ra's Al Ghul was there, perhaps he considered having to kick them out as a kind of "two birds with one stone" thing. I could even see him getting a small amount of satisfaction from it too, though, in a light and jokingly way (again, because he doesn't really care about those people; just Rachel, Alfred, and now Lucius).
As Bruce has made very clear, Rachel is extremely important to him; more important than his family name. You can see though, after he makes those comments, that he expresses a degree of remorse, but that soon changes once he takes notice to Ra's Al Ghul's posse.