I actually had to sit and think about that one for a minute...
My first thought was that they would stay still, but then I thought the reason bubbles rise is because they are less dense than the liquid they are in and are trying to move to a lower-pressure area, so I think that their behaviour would not change in that respect, they would move towards the opening of the glass, because of pressure. But if you held the glass upside down, they would still head towards the opening.
Problem is, then the thought occurred to me that if you tilt a glass of soda, the bubbles still go 'up' relative to the person holding it, not the glass, that might be related to the fact that the gas is less dense than the air outside the glass.
I still think they would head towards the exit, because it is the pressure of the fluid on them that causes them to move, they displace more than they weigh, but I'm not entirely certain of the details, they may even head in every direction, depending on which edge is closest...