If you are going biking you will probably have to spend money. If you are going to go camping and biking it will cost you even more. If you go off-road, don't spend too much to begin. A good bike will get you into plenty of places you will be surprised you managed to get to.
If you plan to go camping via bicycle, don't get a Mountain Bike with shock absorbing fronts or rears. They work well if you are a world class athlete but don't assimilate very well with the real world when it's time to camp and you don't have a group of followers with camera gear and intermittent commercials during the rough times you may encounter. Panniers that will hold everything you need can be purchased through REI or other outfitters.
Scout your routes via car and find campsites judging your daily distance. If you map everything well, you will have a very pleasant trip.
But there's always stuff that goes wrong. That's what makes it an adventure. Adapt and overcome. If you pack right, you'll be cool.