In the UK, the cost of owning a car (without any driving) is about £1000/year.
The similar cost for a bike is about £100 (ie maintenance, replacements, insurance etc).
Once you add in milleage costs, the difference is huge.
The startup costs for cycle commuting are "front-loaded" so you buy all this expensive stuff to begin with then use it for free. Once you get into a cycle lifestyle, you replace worn out stuff as you need rather than in one big hit.
You also have to factor in the costs of fitness, eg gym membership, driving to the gym.

Cycling is cheap even compared to public transport.
Most cycle commuters under-spend. The thing they use most in their life, almost everyday of the year for about an hour or 2 should be of a good quality.
If you spend $800 on a bike, $400 on accessories and kit and then spread the cost over 5 years, you end up paying (800+400+4x100)/5=$320/year or about $1/day.