1. To galavant around under a false identity, usually performing various licentious and immoral acts.
2. To get out of a commitment by pretending to visit a problematic or sick friend or family member. Often, with the time gained from this bunburying, you bunbury do the first definition of bunburying as well.
It derives from Oscar Wilde's "The Importance of Being Ernest", where Algernon invents a sick friend named Bunbury as an excuse to visit the countryside and avoid his relatives. Also considered bunburying, Jack invents an uncouth brother by the name of Ernest as an excuse to visit London and shirk his domestic responsibilities.
"Hey, lets go bunbury in Las Vegas!"
"Sounds good, I think my friend has some serious gambling debts that i must help him with *winkwinknudgenudge*"