To not be of someone's 'thing,' interest, taste or expertise. A polite way of saying that you have no interest whatsoever in what is being suggested or discussed. Can also be used in admitting ignorance of a certain subject.
Compare 'bag' to cup of tea. Perhaps derived from 'bag of tea.'
1. Guy: Want to come to the body building show with me this Sunday?
Gal: Uh, no, that's not my bag.
2. Fellow: Do you know any jazz clubs around here?
Buddy: Sorry, that's not really my bag.
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