There were many different types of bitters that used to be called for in specific cocktails over the years. While Peach Bitters was nowhere near as popular as Orange Bitters or Angostura Bitters, you can still find a few published cocktail recipes that call for this ingredient.
One use I recommend for this unique bitter, is a dash or two to rest on top of a finished Bellini cocktail to add an extra perfume of peach to its delicate taste.

So far, I have only located a single source for this ingredient. And that is "Fee Brothers" in Rochester N.Y. You can reach them at:

{b}Fee Brothers{/b}
453 Portland Ave.
Rochester, NY 14605
USA
(716) 544-9530