A bike lane to the right of a right turn lane is a bad design and warrants a complaint to the director of public works. The bike lane should either shift to the left of the right turn lane before the intersection, or end before or where the right turn lane begins.
In this situation I would shift left out of the bike lane and into the right-most lane that proceeds in my intended direction of travel. If this lane is wide enough to share I would stay off to the right, but in the lane. If this lane is too narrow to share, I would take a more centerish position that makes it plain that there is not room for a car to pull beside me and remain completely in the lane. The heavier the traffic, the earlier this shift in road position must commence.