From the Online Etymology Dictionary:
bunny – 1690, dim. of Scottish dialectal bun, pet name for “rabbit,” previously (1587) for “squirrel,” and also a term of endearment for a young attractive woman or child (1606). Ultimately could be from Scottish bun “tail of a hare” (1538), or from Fr. bon, or from a Scand. source. The Playboy Club hostess sense is from 1960. The Bunny Hug (1912), along with the foxtrot and the Wilson glide, were among the popular/scandalous dances of the ragtime era.
Thanks to Adrienne for making me look this up.