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1.
A gratuitous term for anal sex often used by primary/early secondary school age kids descriptively or as a form of insult.

Can also refer to toadying, sycophantic behaviour in much the same way as brown-nosing or arse-kissing.
Example 1

Kid 1: 'Why were you and Mike in the toilet together?'

Kid 2: 'Dunno'

Kid 1: 'err, bumwilly!'

Example 2

Kid 1: How come Mike got that new PS3 with 5 games?

Kid 2: 'Must have been having bumwilly with his Step-Dad'
by Lord Manhammer July 07, 2009