Green’s Dictionary of Slang

1. to run fast.

1994

C. Major Juba to Jive 214: Greyhound, v. (1940s–1950s) to run fast.

2. to pursue white sexual partners.

1972

D. Claerbaut Black Jargon in White America 67: greyhounding v. dating or socially pursuing a white person; associating across the sexes with a Caucasian.