+1 on taking the lane. I agree with the slow traffic to the right principle but there are times where taking the lane is the safer alternative and a LH turn is one of them. If you don't take the lane on a LH turn, you're practically encouraging the potential knucklehead behind you to try overtaking while simultaneously executing the turn.

The cop was well intentioned but I suspect misinformed (I have no idea what your local ordinances are about bikes on sidewalks). In principle, unless it's got training wheels on it, a bike has no business being on a sidewalk. As far as your gender affecting the exchange, it probably caused the cop to be more of a gentleman and "give out advice" rather than a "reprimand."