My question is whether anyone has success stories or resources for how to hook up a stationary bike (or even a system for a current mountain bike) to a battery and then be able to use that energy instead of using the grid?
You can do it, but the energy generated turns out to be minimal, and you'll never even save enough energy to pay for the battery with a system like that.
My thoughts are 1) it would be a fun project to get off of the ground 2) I'm going to exercise anyway, so why not benefit by $30-$50 per month or more when most gyms CHARGE you that much and 3) if it works well enough, I could potentially even switch a few more appliances to electric from gas in the long run and save even more myself!
$30 at $0.12/kWh power is 250kWh.
A typical human can maintain 100W output for reasonable periods of time. So to generate 250kWh, it's a mere 2500 hours of pedaling. Which is a problem with only 700-someodd hours in a month.
An olympic cyclist can power a toaster, for a short burst, but is pretty well wiped by the end and generates a tiny fraction of a kWh.
So... this is not a project that has any possibility of financial upside.