While cycling is obviously much, much cheaper than a car, I'd argue its a myth to say it's 'free'. Start commuting a _reasonable_ distance regularly by bike and you are going to incur running costs, as well as often not insignificant investment in essential accessories you might need depending on where you live - clothing, panniers, lights, helmets, locks...
There's a fair amount of things on a bike that, like many other mechanical things, can need looking after to keep running well - new tires and tubes, CO2 cartridges if like me you are too lazy to manually pump, chains, cassettes, lubricant, wheels (eventually), brake pads/discs. If you don't have maintenance skills for adjusting things like derailleur cable tension/brakes you will probably need to budget for shop servicing too. It's often considerably more than non-cyclists expect, and often scales with use. If you ride regularly in foul weather, many of these items need attention much more often - there's nothing like road salt to prevent ice for causing just about everything on a bicycle drive train to rust if not cleaned off.
Not doing essential maintenance like chain replacements usually just increases costs in the long term - worn chains in turn accelerate wear on the cassette etc.