So I was incorrect. There are actually a ton of campgrounds on the east side of Bear Lake. The first one is South Eden which is small and reservable and at least the next two are walk-in and quite large but have a single road feeding all the sites. The ones towards the end of the east side, up north on the Idaho side, were not as nice. The last one by Bear Lake Hot Springs was horrible. Just a plain open area with a million people parked in there. There is absolutely no where to pull off the road and just park overnight.
We got lucky and were able to get a spot for Saturday from someone that wasn't using it for their trailer. They had parked next to their friends. We paid them and they let us have it. Same thing came up for the following day in a different site. So overall, it worked out. We just had to move the trailer a little ways each day.
The next two campgrounds were absolutely full on Friday. Ranger said, he ticketed several campers parked in areas that were not officially a site. We did see a handful of available spots at those campgrounds the following two days. Ours was full the whole weekend.
After this exercise in campground comparison, we decided we liked South Eden the best. It's small, yet the site space is big. We got to try out three different sites on different terrain, one secluded by greenery with a long narrow drive, another with no trees, but large and circular close to the shore and one more standard site next to others that were the same. They were all nice.
Drove up to North Beach on Sunday and it was packed with people to the brim. Crazy! So we drove back to our little shoreline by the campground and enjoyed the peace and quiet.
This is right before the sun came up over the mountain behind us.