Perhaps something a bit more concrete would help.
Your costs include getting there and back, which I assume you can figure out.
Also bike preparation and maintenance, which I don't expect you need help with.
The parts that you might not know by virtue of being from afar would be food and lodging.
Lodging I'm guessing the other answers have pretty much covered. As in the cost is all over the map depending on whether you can/wish to wild camp or stay in fancy hotels, or somewhere between. And other than campsite costs (which have pretty much been answered), the rest you'll find at least a good estimate by doing some web searches.
So that leaves food. And of course it depends on how you choose to eat. If you prepare your own food from what you're able to pick up locally, you should have no particular difficulty staying within spitting distance of $10 per person-day. And that's eating pretty well. You could do it on the cheap for half of that, or do it on the cheap some of the time and eat in restaurants with the residual.
If you only eat in restaurants, but you're not looking for anything fancy, you'll find yourself paying anywhere from $3-5 when you luck out to $7-12 when you don't, for breakfast; slightly more for lunch, and it'll be tough to meet your caloric needs and eat healthily for less than $7-10 for supper. Of course if you want the occasional "nice" meal, the sky's the limit depending on what you happen across, and choose to order.