Right turns from left lane

The barrier prevents merging into the bus/bike/taxi/motorcycle lane, so motorists in the next lane must cross in front of through bicycle/bus/taxi/motorcycle traffic when turning right at this unsignalized intersection. The checkerboard pattern in the foreground is intended to warn motorists to look to the right for through traffic when turning right from the left lane. Would it make more sense for bicyclists to ride on the opposite side from the buses on this one-way street?