I actually getting quite good at it. I'm not yet an ace pilot (need to master hitting tanks with the hellfire without locking onto a tracer dart for example), but I'm fairly effective and usually keep the bird up in the air forever.

Is there any part of the single player campaign that lets you fly one?  I'd like to learn, but not at the expense of an entire team/match.

No. I leave it to more qualified players. 
 
I did snipe a pilot before which was pretty cool.