That can happen if the bird shot sits on a perfect paint surface for a little while. I have had black cars in the past, and the same thing has happened on various occasions. You should get used to the idea of carrying a spray bottle of water with you in your travels. It is VERY handy in spot situations.
Additionally, you may want to try one or two medium abrasive polishes or paint cleaners (give gliptone's pro-buff a try...it is a very active paint cleaner).
You could also, if it doesn't bother you, wait it out. I have found that if the bird spot wasn't too severe, in time the spot will dissipate. How....don't ask me, but my very few spots over the years in time have vanished from my surfaces (with my traveling water bottle, though, it will be a very hard task for a bird bomb to take residence on my paint surface.....but as the saying goes....sh*t happens!).
PS: One more thing....never attempt to wipe off poop with a dry towel. Always wet down the spot. Some bombs can be as abrasive as needles, as I had found out on one unfortunate occasion.