Green’s Dictionary of Slang

dog, the n.1

also gray dog
[play on proper name]

(US) a Greyhound bus.

[US]Hiler Monkey Mt. 160: Always the bus. Jesus, I got tired of ridin’ the Dog [HDAS].
[US]Eble Sl. and Sociability 81: The Hound and the Dog for Greyhound bus are associated with African Americans and students, though they originated among truckers.
V. Hendricks Voluntary Madness 73: I’ve ridden the dog before, once all the way to California and back.
[US]N. McCall Them (2008) 93: He [...] trudged five miles to the bus station and caught the gray dog to Atlanta.
[US]J. Stahl Happy Mutant Baby Pills 52: Riding the Dog. When’s the last time you traveled by long-distance bus? Or sat in a Greyhound station?