During my transient life, hopping boxcars (ooops, that wasn't me), I have encountered some unsavory people. I picked up a few phrases unique to certain settings. One, in particular, is the seemingly proper noun, "My Old Bitch".
I decided to research this but, finding little credible data, I decided to write what I think it means:
My Old Bitch, archaic form of a proper noun. Origin: Jerusalem, in a stable, circa one hour B.C. (Blasphemous slang)
Modern interp: 1. A female dog 2. a horrid woman. 3. A nickname given by an uncouth male, to his spouse or significant other whom is a perfectly nice woman that refuses to leave the uncouth man. {Definition #3 is often followed by the woman say, "You aint gettin' any, tonight."}
My Old Bitch can also be used in place of "...the wife of a junkyard dog..." of either canine or male human type.
"Old" is generally not used as a measure of age, but merely a term of un-dearment.