Of course you can do it!

Don't worry about super long distances; most day's mileages will be governed by the spacing of towns or suitable camping spots. Wind can also be a factor. Work your way up to being able to handle 50 miles, and you shouldn't have a problem. It may sound like a lot now, but if you keep going at it like you are now, you will be knocking that out in short order.

One of the routes Google maps recommends heads north out of Riverton to Shoshoni, then Highway 20 toward Casper. My wife and I rode that section of road as part of a longer tour a few years ago. While it does not show any facilities on that stretch of road there is a great state rest area, Waltman Rest Area, that we camped at, and there was a store not too far from it. If you decide to take that option let me know and I'll ask my wife to dig out her journal for the trip for distances, locations, etc.

Good luck in your adventure, and keep us posted