The provably fairness in bustabit does not strictly have as strong guarantees as the ones in well designed single-player game (e.g Just-Dice or PrimeDice's), however it would be a mistake to think it's not provably fair. In fact, there's a whole thread on it's provably fairness: https://bitcointalk.org/index.php?topic=922898.0 and I haven't heard a suggestion that could make it any stronger than it is, I think it's best-in-class for a multiplayer game.

But 99.9% of the "complaints" on bustabit are that I'm manipulating the busts to make them lower, which the provably fair disproves. So I don't think you'll have an issue =)