Simply nothing happens when a bird strikes a hot air balloon. To begin with, a balloon is rather big and sluggish. As a result, attempting to surprise an animal with a balloon is quite difficult. In the unlikely event that this does occur, the bird will fly into the balloon and bounce out immediately.
Ripstop nylon air balloons are not pressurized, do not pop like latex balloons, and can withstand considerable abuse while still flying. A balloon will also not deflate or lose altitude as a result of a hole any bird could make in it. Balloon manufacturers have performed tests, and it is possible to fly a balloon even with a hole.