Billious is probably a psychopath. Mrs. bill is the sociopath. There is a difference in the origin of them but not in the result.
Well, I tend to trust my mom with these things. She worked special education for most of her teaching career (master’s), specializing in emotionally disturbed kids, spending much of that time in charge of high-school students’ education in an institution.
Of course, not actually encountering the bum, she could be wrong. Her view is from afar.