Connected to the bathroom? As in on the same breaker? Or wired in line/series? If they were wired in series any GFCI's in the circuit path could be causing the problem. Which creates the headache of tracking it down. If they are wired in parallel this wouldn't be the case and the fault would be the BBQ. Check the outlets to make sure they are wired in parallel. If it was jerry rigged it might be in series. A house should always be parallel IMO, but I have seen weird stuff done by homeowners. Coat hangers to hand 80lb flourescent light fixtures comes to mind.
Not my pic but works to show what I mean
http://i30.photobucket.com/albums/c3...UFF/lights.jpg