Wordorigins.org

This term for a lesbian is a clipped form of bulldyker, an American slang term that dates to at least 1906. The origin is unknown, but the fact that bulldyker is the earliest known form by several decades limits the possibilities significantly.

From J. Richardson Parke’s Human Sexuality (1906):

In American homosexual argot, female inverts, or lesbian lovers, are known euphemistically as “bulldykers,” whatever that may mean: at least that is their sobriquet in the “Red Light” district of Philadelphia.