Green’s Dictionary of Slang

bitter mouth n.

[rare and mainly southern; talk that ‘leaves a bad taste in one’s mouth’]

negative, cynical speech.

[US]M.H. Boulware Jive and Sl. n.p.: Bitter mouth ... Talking smart.
[US]C. Major Juba to Jive 37: n. [1930s–1940s] related to ‘bad mouth’ and the idea of a bitter tongue; ‘bitter mouth’ refers to cynical or mean talk.