If you do not enter the bike lane before your turn, for whatever reason, it is a violation to make the right turn across the bike lane.
§ 141(1)(2) of the Highway Traffic Act says:
Where a driver or operator of a vehicle intends to turn to the right
into an intersecting highway, he or she shall, where the highway on
which he or she is driving has marked lanes for traffic, approach the
intersection within the right-hand lane or, where it has no such
marked lanes, by keeping immediately to the left of the right curb or
edge of the roadway and he or she shall make the right turn by
entering the right-hand lane of the intersecting highway where the
lane is marked or, where no such lane is marked, by keeping
immediately to the left of the right curb or edge of the roadway being
R.S.O. 1990, c. H.8, s. 141 (2)
The bike lane is a lane. I am frustrated that I cannot find a definition of lane in the Highway Traffic Act but I did find in the Toronto municipal code:
BICYCLE LANE - The lanes or portions of lanes of highways designated
as bicycle lanes under §886-8
So if bicycle lanes are lanes, and you must be in the rightmost lane to turn right, then you need to be in the bike lane. It is definitely confusing and perhaps impossible sometimes!
In the US the typical rule is the as you've described - cars, yielding to approaching bicycles, move into the bike lane to make right turns. As you've intimated in your hypothetical, it causes all sorts of problems.
As for the law around taking a right turn from an area to the left of the bike lane, that's going to be up to the discretion of the police officer and then perhaps a judge! What is a driver to do who approaches a right turn at a red light with no cars waiting, wants to move into the bike lane, but the dashed line hasn't started yet and the bike lane is full of bikes. The driver can't go into the bike lane (solid line) and can't pull forward to the light (must be in bike lane to turn right!), and can't roll up to move into the lane after the dashes start (full of bikes)!
Fact is, drivers come in three flavors - those who know how the bike lane turn rule works and try to follow it, those who don't know the rules but see bikes and try to do their best, and those who don't know the rule and don't see bikes and do whatever is in their best interest.
Even better is these biker boxes that they are painting in some places. These things are not even defined in the laws or the driver handbooks! So they are painted on the roads, but can drivers be ticketed for somehow not doing the right thing?