rabies cannot be passed down via bat poop Guano or bat urine the same goes for all mammals that can contract the virus, rabies can only be contracted by the saliva of a rabid animal.
i too was scared of getting rabies from a bat i understand what your going threw, i was scared of nothing as the bat din't even touch me just flew over me, and the fact that it is flying perfectly would indicate it doesn't have rabies as a bat with rabies would be unable to fly.
which is where people would get rabies by handling a downed bat with out the correct protection.
also if the bat spat on the stick the rabies virus would have become defective within a few seconds to minutes and the chance of that happening is very low as bats don't spit, and rabid bats don't foam at the mouth so they would not drool onto the stick.
so you have nothing to worry about.
hope i could help relief your anxiety if not just say so and ill see what i can do to convince you that you don't have rabies.
be safe around wild animals don't approach them.
and i can assure you, you do not have rabies.