Can I grow a plant from a flower bud that fell off?
Normally I wouldn't even think to do so but this one has a green bud. Is it possible to put it in some water or plant it?
Amy I'm not sure what it is, but it appears that there is a seed formed at the base of the flower. If that is the case, maybe the seed will sprout. Otherwise it is not normal for a flower bud to sprout, you need a seed, or a stem for vegetative propagation.
If you post again with with a photo of the entire plant, we may be able to identify it and give better advise on propagation.