I myself never really thought their relationship would go any further than friendship, of course I have considered it a few times. However, watching Z before the original DragonBall it changes my perspective on things - I've known and got to know Goku and Chi-Chi being together. Even if Bulma got to Goku before Chi-Chi did, as soon as Vegeta appears I think Bulma would have changed (providing that everything else remained the same, no Gohan being born may have changed things with the kidnapping). In the Buu arc we have Bulma really expressing her feelings for Vegeta, just as she does in the History of Trunks special.
If Bulma was able to lose interest in Yamcha, I really think it would have been the same when Vegeta came along - though Bulma really matures by that point.
It's hard to call because it's not real life and we can't judge it like it is because plot can change everything. I always really liked the Goku and Bulma friendship because they were the first ones of the whole gang to meet. On top of that, Bulma was always the one that thought back and told the stories of what it was like when he was a kid - from these points it really makes me feel their friendship is strong.
I like their relationship as it is

. Also, Goku showed us his resistance to women when he said he "doesn't wanna see no dirty butt" of hers - therefore I conclude it would have never worked.
