Hello,
Not a St. Bernard owner, but have had dogs my whole life. This isn't so much a chicken/duck/dog problem as a training (or lack of) problem. Your pup doesn't have a "taste for blood", she has instincts, prey drive. The birds are prey in her mind, and chasing them/ catching them is instinctual, and, most likely, fun.
From your post, I would highly recommend seeking out obedience classes/lessons for your dog from a professional. I don't know where you are located, but you can google and see if there is a local AKC club in your area, or contact your local shelter, pet store, dog groomer, etc. to find a trainer. And the reason I highly recommend this as, you are lacking control of a puppy, who will grow into a large dog, and could possibly really do some damage if you don't take the reins now. St.B's are fairly easy to train, and with a trainer, you can nip this quickly.
Best of luck to you and let us know how it goes!
BTW, sorry to hear you have lost some birds

It's very heartbreaking to see or find!