Ive camped all over the country like this before. Its actually really easy I have found. Its obviously not as convenient, but its not an issue really. Ive never been in trouble, asked to leave, or move, or the cops called. So its not an issue to "hide out"... For me its not about necessarily about the cost of staying at National park, its just that im tired, need to get off the road and there is no normal camp ground around. Then I just pull off the road and go find a spot. IMOP, I think there are "rules" to fallow. If folks don't know the "rules" you will find out. These are not in a hand book, these are common sense street smarts 'rules'.
On one occasion, one of the most fun was a 100 mile dirt road out in West Texas. It was probably 4-5PM when we started looking for a spot. Within 15 minutes we found an abandoned oil/gas location dirt road entrance. The gate was open, all the official tags were removed off the fence, Etc. We pulled in and road about 2-3 miles down a dirt road to an old dried out "farm pond". We road to the bottom of this very large pond and set up camp. It had a large ring of dead trees around the old pond and tons of fire wood. We had a great fire that night. Two tents, two bikes, no issues. It was really awesome. Packed up the next day and kept on with a Texas ride called the "Lubbock Loop". (off road loop around Texas)
Watch out for purple fence post, don't be "that guy"...
Once I was riding the AZBDR. My buddy and I were camping off the BDR trail up in the mountains of Arizona. It was used as a camp site and it was very obvious because of the fire rings, Etc. We were about 25 miles off a dirt road and 30-40 miles from any normal "town" for fuel. OK, here is what to always be aware of. The 25 miles are on dirt roads, up a mountain. Not typically for normal cars or typically normal people in normal cars for a Sunday drive. (this was not a smooth dirt road this was Off-Road) We were all set up and cooking dinner and there are some folks that were not of the savory type stopping at the entrance of our little camp spot. You would have had to been there, but what cross my mind was nothing good could come from these people. SO- in a case like this you (Im) prepared to have an 'emergency exit' if necessary. You're never in control of people that want to do you harm. 'street smarts-rules'. In this case they pulled up sat there for a good while and then kept going up the mountain to no where. (we are out in the middle of BFE off dirt road mountains, no reason for this type car / people up there) These people came up the mountain for there own 'business' and maybe we where in there meeting spot ? They were way out of place, very obvious. You just have to keep your eyes and ears open the whole time. If non of this sounds like your cup of tea- probably best to camp at the park or motel.
Ill also add, like Checkswrecks said: I had a situation one time where I came to a popular city camp site. They were "full". When I walked up to the office she said they were sold out. I politely asked if I could put down a tent for one night just right here. I pointed to a small green grass area right near the office.. I quickly offered to pay if I could. She said "SURE", you just wont have power. I said "no problem". I still had a really nice place to sleep in my tent and a hot shower. My thought is this, even if the front sign says full or sold out, it still might be in your best interest just to ask.. Ive NEVER been afraid to ask any question. What is the worst that could happen....... someone says NO... LOL Once again, it worked out just fine !