Ideally, you would be correcting before she gives chase. You will have better results if you correct the intent to chase rather than the chasing itself. Look for the subtle signs that come before the chase, tensing, hard stare, stalking posture, alert ears and tense mouth, etc.
I would again recommend the use of a remote collar. It would not be even remotely (pun intended) acceptable for one of my dogs to take a bird in their mouth, regardless if they don't actually harm it or even drop it when confronted.
Do an internet search on "crittering" with a remote collar. Look also for videos on boundary training with a remote collar, many of the principles are similar to how you would train for crittering.
Get a collar with at least 100 levels of stim so you only have to use as much as effects you dog's behavior. Condition the dog to understand that the stimulation means the same as leash pressure. Once that is done you will be able to communicate with the collar even more effectively and timelier than you could with a leash.
A good resource is
www.loucastle.com as well as
www.dogtra.com and Robin McFarland's site
www.thatsmydog.com