When I'm riding on a sidewalk (a rarity) I go down to pedestrian speeds. Any bike rider with a modicum of experience can easily gear down to pace pedestrians in a split-second.
Unless your bike is motorized, that is.
Maybe half the car drivers in this city are willing to hit the brakes when confronted with the choice of slowing down and waiting to pass a bike safely and just trying to slide by, hoping the bike doesn't hit a bump and careen into your right side-view mirror, or under your bumper.
I generally just don't take the chance. If I deem there isn't room to safely pass me, I position myself so that the car doesn't have the option. Either he hits his brakes or he runs me down. When given that option, so far 100% of drivers hit their brakes. Though this tends to piss people off, it generally just means they are inconvenienced 2 or 3 seconds, which they easily make up after they safely pass, and are back to tail-gating the car that was in front of them in no time.