How can you play your bass with small fingers?

Yes. It might make things a little more challenging and you may never be able to do the super-complex stuff, but if you don't let that keep you from enjoying it, i don't see any reason you couldn't be a successful bass player even if you are missing a couple digits.

It depends which hand is missing a finger. If you are right-handed and it's your right hand, you'll be pretty much fine, but you might have trouble if it's the left since bass frets are notoriously large and one wants all the fingers one can get. However, I see no reason why you shouldn't be a perfectly capable bassist - and it is generally possible to train oneself to fret with either hand, providing one has discipline.