Bird droppings are acidic are can severely and permanently damage your paint. Hence the importance of having a quality sealant on your car.
If you car has no protection, bird droppings can quickly eat through your clearcoat and into your paint resulting in a "permanent" stain.
Your best bet is to try using and polish with a proter cable or orbital to try and get it out. If you see no improvement, you can step up to a more aggressive polish. Possibly even a compound. If you have any experience, wetsanding (not recommended for those with no experience).
You may have to take it to a body shop/professional detailer and have them take a look.