If you can rely on a bicycle for most of your day to day traveling, you'll save money in all sorts of unexpected ways. Most obvious: the gas you'd have needed to drive to work or to the store. If your daily driving uses up 10 gallons (38 liters) of gas each week, you'll save $30 to $40 every week by riding your bike. You can cut out the costs of car insurance and car repairs, not to mention the price of a car itself, if you can rely solely on your bicycle for transport. That's a difficult step to imagine, but you'd save thousands of dollars each year.
Public transportation is another alternative mode of travel, but riding a bike has advantages over that, too. A monthly bus pass costs between $30 and $105, depending on the city. Wouldn't it be nice to cut that expense out of the budget?
There's one more potential savings factor if you ride your bike everywhere. You might be able to skip the gym membership, since you'll be getting plenty of exercise just getting around town.