I found that camp site costs varied, but averaged at $10 - $15. Motels probably averaged at $80. Food probably runs $10-15 a day if you rarely eat in cafes; $40 if you favor letting others cook for you.
Totally self contained, assuming 80 days = 80 * 25 = $2000.
Totally credit car, probably 70 days (faster) * 130 = $8400. But free places can bring that down.
As for your bike - 15 years ago, getting to a 1:1 ratio (your 26 x 26) was the holy grail - heck, many of the original Bikecentenial riders did it on Schwinn Varsitys with 42 X 28 gearing. And back then, a rear rack stacked high, plus a handlebar bag was it. We tend to think now days, that a brand new Surly Long Haul Trucker with Tubus racks and a matching set of Ortlieb bags is needed. It's not.
One note on hotels in Yellowstone - most of them sell out months in advance, and that's at $200 per night. Elsewhere is easier, though 4th of July can be a challenge for both camping and motels.