Cotton Burr compost is made from the waste material left after ginning cotton. Since cotton is mostly a very heavily sprayed (pesticides and herbicides) you may want to consider other compost.
The "composted" manure from most commercial sources comes from the Confined Animal Feeding Operations and it probably is just manure that has been sitting around for quite some time and then bagged. Since htese animals are feed large quantiites of antibiotics, to promote growth as well as control diseases, this manure can be full of them and may not be something you would want to consider either.

i bought some bagged 'compost' one time, and it was harder than my soil. I could stomp the dried clumps and they would almost hurt my ankle, they were like bricks.

See if you can find the source of the composted materials. For example, a big compost place in tennessee simply piles up the litter out of their huge horse barns into widrows, then they compost it.

Of course, starting your own pile is the best compost you can get.

Since there is nothing that regulates what can be sold as compost, like "topsoil", what ever is sold as "compost" can be anything. If someone wanted to sell brick dust as "compost" there is nothing that prevents that. So purchasing, from any store, any kind of organic material is truely at buyer beware situation.

Try the local landfill. If you have yard waste pickup in your area then it'll likely go to the landfill where they compost and sell/give it back.

Besides for the quality issues, buying bags of compost to cover a lawn just isn't practical. It takes about 1 cubic yard of compost to put a thin layer on 1000 sq ft of lawn. Say you have a 5,000 sq ft lawn. That would take 5 yards of compost. A bag of compost from HD is usually 1 cubic foot. There are 27 cubic feet in a cubic yard. That translate to 135 bags to cover a 5k yard.

If you are going to use that much compost, it is much easier and cheaper to just have a local company deliver a truck full to your home. Some cities have composting sites that are quite inexpensive, but then you need to get it home somehow. 1 yard fills a full size pickup truck bed.