Bitch lip is a phrase in which a person packing a lip (doing smokeless tobacco) takes a tiny pinch that is almost unrecognizable as an actual lip. Comparatively, a bitch lip is the opposite of a "mouthpiece" or a "upper and lower mouthpiece". In the former, said person dipping packs the lip throughout the bottom teeth all the way from the front to the molars in the back; in the latter, the idea is the same, however both upper and lower teeth are packed (the almighty grail of dipping).
Ryan: What are you a girl doing that bitch lip?
Jake: What do you mean?
Ryan: Shut the fuck up... Unless you be a man and stop doing that bitch lip, repack with an actual lip, or go all out with a mouthpiece, I don't even want to be seen with your ass...
Jake: Ok, pass the tin...