That depends on the state. In Maine, for example, a driver is supposed to make a right turn and approach while as close as practicable to the right curb, which means merge first into the bike lane. Here in Georgia as well you turn right from the right-most lane, including the bike lane for as much as 200 feet.

Evidently many motorists are confused by bike lanes at intersections and unless they know the specific law in their state it does seem contradictory. Right turns, generally, are safest when you don't leave room for another vehicle on the right, including a motorcycle or bicycle. Ideally the bike lane should be between the right-only lane and the straight through lane, although the transition can be tricky.

Bingo! As mentioned, same in California. It sounds as though most states get it right, with destination-appropriate lateral positioning. If a motorist is turning right, I want him to merge -- cautiously and without violating my right-of-way, of course -- into the bike lane on final approach, leaving me room to move to his left. This discussion probably belongs in A&S, where I am sure the topic has been covered endlessly.

If I am driving a motor vehicle, you will not find me in the bike lane. It just isn't going to happen. We need to have one national standard and stick to it. Motor vehicles stay out of the bike lanes. Especially at intersections.

As long as the cyclist is riding sensibly, taking the lane behind you when approaching the intersection, you should be OK. If he's hugging the curb and expecting you to turn correctly he may not expect your turn from the wrong lane and you could hook him

I would not hook the rider, because I always look to my right for cyclists.., because this is where they ride: To the right of traffic.
A rider should go out in the traffic lane, "taking" the lane to the left of the bike lane.., so that the car in front of him can use the bike lane.., because the driver can not execute the turn in the area of the lane she occupies?