North Monroe Street has the narrowest turn lanes in the known universe, so this can get a little unnerving when there's busy traffic going north and south. A safe and sane way is probably to ditch Monroe and ride into the parking lot across the street (if it's not blocked by a line of cars as it is in this shot). Another option is to cross one block north at Broadway, but it has one of those long red lights. Sometimes I stay on Monroe and cross the bridge, especially if I have trouble getting over to the left lane, but it takes me a little out of my way.
(oh boy, youtube has found other videos to watch titled threading the needle. remind me not to use youtube again. although )