Right turns should be made from a position as far to the right as possible. It is legal (and correct) to enter a bike lane when making a right turn provided you first yield to any bicyclists using the lane.
Prepare for your turn in advance. Check for bicyclists ahead of you and behind you as you approach to ensure it is safe to move over to the right. Use your turn signal to indicate your intent to turn.
Tips for Bicyclists:
Don’t pull up to the right of a motorist that is giving clear intent to turn right (signaling, slowing etc.)
Understand the law and know that right turning motorists may use the bike lane. Wait behind right turning traffic or, if there is adequate room and you are proceeding straight, pass to the left of the right turning traffic.