Oh so you've watched more than I thought you did. XD
I must admit I'm a Bulma/Vegeta shipper, even though I keep pairing Vegeta with Goku or Gohan (though in my most recent fic he's definitely together with Bulma as well).
My theory on the Bulma/Vegeta thing comes down to sex really. Especially the first time, I honestly believe she probably put the moves on him, and he let her continue or followed through with it. One night stand and all that, or perhaps a several night stand until he was like "okay no more distractions, also wtf she's pregnant" and took off.
Frankly Vegeta is probably VERY GOOD in bed. Plus, after he settles in a bit, it's probably reassuring to have someone around that basically acts as the best bodyguard ever. No one is going to attack her or her family. EVER.
Finally they're probably both very good at ignoring each others egos. Bulma doesn't cower at all when Vegeta gets... Vegeta-like (she just gets annoyed), and Vegeta can't blast her because then he wouldn't have a nice place to live. (also if he did blast her someone, whether Goku or Gohan would come and put him in his place and/or kill him. So, gotta keep her alive.)
As for the reason why I think she ended up growing on Vegeta so much (besides their shared child) is the fact that Vegeta's literally never had anyone care about him before. I don't think Nappa counted, he was a Saiyan who loved violence just as much as he did, but Bulma for all her rantiness does care like most woman would. I imagine (and I've written this) that he is different around her in private than when he is around the other fighters, not completely different in personality, but more tolerant and they'd be able to have intellectual conversations, since they're both rather smart. Yeah sure, he'll never give her hugs, but if you have someone to talk to/argue with and who is phenomenal in bed all could be forgiven I think. ;)
Just my thoughts. You've been reading the fics, you know this stuff already. ;)