How do I prevent burning the bottom of the bread when cooking over a campfire?

Many camping cookbooks recommend picking up some coals from the fire and putting them on the lid of the dutch oven while it is on a grate above the fire. This gives a more "all around" heat rather than just trying to cook the whole loaf of bread from the bottom. This image search gives lots of examples.

Personally, I don't try to bake a whole loaf of bread - I make English muffins. Quicker time to edible food, easier cleanup, you don't need to carry a heavy pot since the frypan is coming anyway, and if one burns the rest might still be ok, so less risk. (Important when you're feeding your children in the wilderness.) I wrote it up with pictures long ago - see if that helps you.

Coals on the lid will help. I put a flat stone in the bottom to bake on like a slate in a pizza oven. You could use a rack if you are cooking in a pan. Either way keep it off the bottom. Parchment paper is too thin, you have to dissipate the direct heat.

Your fire was probably too hot at the bottom, and too cold at the top of the dutch oven. Was it flames or coals and ashes? Only the latter will do correctly.

You can heat the dutch oven (including the lid) before you put the bread inside, to make the temperature more regular. Turning it 1/4 of a circle every 1/4 of the time also helps having a more homogeneous temperature and less black spots.

As a workaround if you only have flames or are in a hurry you can better insulate the bread from the oven's walls by adding a layer of cardboard where it would burn without additional insulation. That will avoid the bottom burning and allow it to cook nevertheless (because of the inside temperature of the dutch oven).

For Dutch oven cooking you need a ground based fire, no grates or other structures

When the wood or charcoal is burning pure (no smoke), scrape away a mound of coals from the main fire. The amount depends on the type of wood and the time required for cooking. For a typical hardwood charcoal around 4 l per half hour (1 US gal) for typical recipe in typical Dutch oven

If your Dutch oven does not have a rim to hold the hot coals, just invert the lid. Place slightly more than half the coals on the lid. Then place Dutch oven over other half of hot coals still on ground. They should have be scraped into a tidy flat shape the size of the oven

Take temperature readings every 20 minutes or so and adjust coal level for your recipe. Use a long metal stem digital thermometer and just poke it under the lid without lifting the lid fully off

This answer pertains to your second question--how to reduce burning on the bottom of the bread.

Cracked wheat or some other course grain, sprinkled on the bottom of the dutch oven before putting the bread in, will slow down how much heat absorbs from that direction. You'll notice this sometimes with store bought sourdoughs. This gives more time for the sides and top to cook before the bottom burns.

Notes from Elizabethan England suggests wrapping the loaf in a cabbage leaf! Will try it along with heat on the lid. Don't know if it will flavour it?