I'm not a fan of Bridget, because it sounds like a frog noise to me, but I'd take it any day over Bridie or Birdie.
Birdie isn't even a name to me; it's what you might call your pet parakeet if you had no imagination, or at best a nn for a small, birdlike person.
Bridie sounds like a cutesy name for a bride, like hubby or wifey. Ick. And it also sounds like a sstereotypical Irish servant character.
Before you criticize a man, walk a mile in his shoes. That way, when you criticize him, you're a mile away and you have his shoes!
Steve Martin