I have toured over 5000 miles on long cross-country bicycle trips, over deserts, high mountains and through all sorts of remote areas, not necessarily friendly towards bicyclists. I have been shot at three times (they missed). You must be ready for any contingency, mechanical or otherwise, or you will be at the mercy of strangers.
Use front and rear panniers and a handlebar bag to evenly distribute the load.
Carry spare spokes and a spare rear axle. Also have spare chain links, a spare tire or two, extra inner tubes and a patch kit. Bring tools for everything on the bike and know how to use them. If you don't know how to use a spoke wrench and how to replace spokes, learn, otherwise you can quickly ruin a wheel. Those who travel large distances on bicycles with camping equipment need to be expert bicycle mechanics.
When you pull off the road to camp for the night, make sure no cars are coming and no one sees where you went into the woods.
Learn to take a bath with a pint of water. Use a water bottle bidet to keep your crotch clean.
Stop at convenience stores where you can see your bike outside. Lock your bike and disable it. Carry freeze-dried food and supplement it from convenience stores. Occasionally stay at state parks where there are showers. Take your bike into the bathroom. Once in a while splurge on a cheap motel, and decent restaurant food.
Always have enough water for the next 50 miles, and fill all water containers before you camp for the night.
Attach a good rear-view mirror to your helmet. Always wear your helmet when riding.
Use cycling shoes with cleats and have alternate shoes that you can also ride in or use for walking. Have surf shoes for wading in rivers and lakes.
Carry neosporin ointment, rubbing alcohol and a small "surgical" kit with a razor, needle and tweezers.
Bring biodegradable soap to wash your clothes in streams.
Use a gasoline camp stove which will run on unleaded gasoline from gas stations, and keep gas in a nalgene bottle. The gas station attendants will get a kick out of you pulling up to their pumps and getting a quarter's worth of gas.