This depends on what you're measuring.
If you take what I spend on bike stuff and compare it to the gas and maintenance that I would be spending to go the same number of miles in my car, yes, I've saved maybe $5000 in the last 8 years.

If you count opportunity cost, I spend an extra 45 minutes a day commuting by bike rather than car. If I worked those hours instead, I would be making an extra $8000/year or so, so bike commuting is a huge financial loss.

But if you then count the fact that I'm a lot happier and healthier and will probably live at least a few more years and be healthier in those years, then it's back to being cheap again.