Need a quirkiness: say your hero/detective, Martha Mavin, is a lady librarian--quiet, shy, bookish--yet she owns a Harley, say, and is the mascot for a motorcycle gang on weekends. Etc., etc.
So how did she ever get involved with a motorcycle gang? It started with her brother, who used to take her riding, and when he went off to Vietnam, he left his bike behind. When he never came back, she started riding to bring back the memory of her brother. She rides with his old gang, who are hard guys, outlaws, but not criminals, who think of her as a kindred spirit despite her bookishness.