Bad and bum are modifiers in the terms bad rap and bum rap, and they pin rap with a negative connotation. A bad/bum rap tends to mean that a person or thing is unfairly or undeservedly being punished or criticized. "Opossums get a bad rap because of their tail.

What does it mean to get a bad wrap?

A bad wrap is an unappetizing sandwich made of fillings wrapped in a tortilla. A bad rap—otherwise known as a bum rap—is dishonor resulting from false accusations or trumped-up charges. No hyphen is needed in this noun phrase.

What does it mean to give someone a wrap?

enclose something in cloth or paper: wrap a gift; the end of filming or taping of a show or scene: That's a wrap.