If you plan well, you can certainly get by without cooking in Yellowstone. Budget accordingly, as even the grill meals can be a bit pricy (especially for the extra calories cyclists can eat!).

By far the best deal in the park is there souvenier extra large size soda cup. It cost 3 or 4$, but I had free refills for like 4 weeks this past summer! Hopefully it will still be around when you go!

Also double check which campgrounds have equipment restrictions just before your trip. When I was there, they were not allowing any soft sided camping (tents/pop up trailers etc) at Fishing Bridge campground due to bears. Only hard sided RV's there.

The other campgrounds I stayed at there had nice bear proof boxes, which you share between a group of campsites. I was on a slow drive out to the west coast, so just kept foodstuffs in my car.

Have fun!