An essay on Vegeta and his social habits! This is probably going to be very disjointed and possibly spoilery, if you've never watched or read Z all the way through.
Re: Vegeta and Being Forced to Socialize
I know I haven't even had Vegeta for that long--less than 3 months and just shy of 1,000 comments--but it had been kind of bothering me initially at how his characterization was coming out. I apped him from about the same time as Gohan was taken from, give or take a couple of days, and yet... most of the threads made me feel like he was coming from an earlier point in time than that. This stressed me out a little bit! But then I came to terms with the fact that without anyone else from canon but Gohan around, Vegeta is likely to regress into his "old" asshole self.
The circle of companions in DBZ really isn't that large, when you stop to think about it--there are a dozen people tops, including his family, that Vegeta is really familiar with. Not having them here is getting kind of hard, because we know he's not the most social butterfly in the universe. Basically, he's having kind of a relapse in behavior: the aggression is resurfacing a lot more again, which Bulma had calmed down a lot over the decade-ish that she came to know him--one remark from her made him rethink his comment about blowing up the reporters at the tournament in canon. Without her or Goku around to really be able to get a handle on his temper, his old tendencies are resurfacing a bit more.
Vegeta and Specific People
This is kind of why he took to Bat. From just a bit later on in the tournament saga, we know that his evil streak is still running somewhere inside--there are a ridiculous amount of subtle-ish hints as to what shit is about to go down between Goku and Vegeta because of Babidi's sorcery. Vegeta knew off the bat (hurhurhur) that Bat wasn't a goody-two-shoes kind of guy, but it didn't really bother him because he didn't feel threatened in the least. (Even if he did, Vegeta would like to think that he could crush Bat if it needed to come to that.) But I don't think I would go so far as to say that Vegeta would consider Bat a friend, or even an ally--he just enjoyed the conversation and story. That does say something, though, when Vegeta doesn't walk away from a first meeting with a feeling of annoyance.
And speaking of annoyances, there's Dante. I believe I've mentioned in passing elsewhere that Dante is Vegeta's new Kakarot. It's gotten so much worse now. Vegeta absolutely hates everything about Dante: his personality, his vulgarity, how he freaking heals instantaneously--even Kakarot can't do that, okay. It really pissed him off when Dante walked away from that fight without a scratch left on him, and Vegeta himself was very worn out--and in Super Saiyan fighting mode. ...and when Dante got Vegeta-in-Bulma's-body drunk and carried her back into the capsule house. Basically everything Dante has ever done to Vegeta has made him feel like a complete idiot, and if an egotist doesn't hate that above all else, I don't know what they do. I don't know if Vegeta will ever really consider Dante a friend like he eventually does with Goku, mainly because those two personalities are so different. He wants to beat Dante in a fight just as badly as he does Kakarot, but I think that's the only comparison they have.
The other major player in this is Harper. I've mini-essayed on him before, but I think he still warrants a spot here. Harper is the only ex of Bulma's (his Bulma or not) that he's ever really had to deal with because Yamcha is kind of a pussy and just tucks his tail between his legs. So when Harper just matter-of-factly stated how long he'd dated Bulma, it pissed Vegeta off so much that the only way he knew how to react was to punch him in the face. What a nice introduction. If it weren't for the fact that it was established that Gohan knew Harper and would therefore prevent any future attempts made by Vegeta to maim him, he probably wouldn't have gone along with the truce so easily. There is also the other side of the coin with Bulma and her effect on Vegeta--he still knows that he would get an earful from the woman if he decided not to go along with the truce, and it probably wouldn't be worth it to risk beatings from Gohan and her.
And... pretty much any child in camp will leave Vegeta a little lost. He has never spent time/watched children that weren't either Trunks, Gohan, or Goten, all of whom are fighters as well, so he doesn't really know how normal children will play or react to him. The drawbacks and benefits of being a main DBZ male. :|b