Aside from the occasional inconvenient puncture, and the initial investment, bikes work out really, really cheap. But as well as that they are much more convenient for getting places than buses (no waiting around) and often you reach your destination quicker, as well as being more in control of how long it is going to take you, and never having a walk either end.
I still get buses for longer journeys (or in the case of yesterday when I got a puncture), but so far this year we have only spent €110 on leap card credit , so really have made quite a saving since I would have been spending €20 a week minimum on buses.