When I used to commute into the centre of Edinburgh the motorbike was way quicker than anything else. The pushbike was quicker than the car in rush-hour, but slower at other times. The bus was never great, despite just needing one bus to the centre of town and with the stop close to my house. I'm not a particularily agressive filterer on the motorbike either, however I mostly used trail bikes which can fit into most of the same places that push-bikes can.
My current commute is short and the roads quite quiet so the motorbike and car take the same time, and the push-bike is slower. Not that it's that much of a difference as we're talking 8 minutes in the car/motorbike compared to 15 cycling.