Bearding is primarily a problem with the batting. Needlepunching reduces the chance of bearding, but does not entirely eliminate it. Wool used to beard terribly (quilters had to encase the wool batt in cheesecloth before using it) until manufacturers such as Hobbs and Quilter's Dream perfected needlepunching. Those two brands of wool batting are now very stable. No matter what the fiber content of the batting, it's best to stick with well-known brands that do not have a history of bearding. You can Google to find horror stories about bearding and then avoid whatever batting was used in the horror story.
Hobbs 80/20 is 80% cotton and shrinks about 3%, similar to all-cotton battings. It can be pre-shrunk, though. Whenever pre-shrinking a batting it's a good idea not to agitate. It's more a pre-soaking than a pre-washing. You place the batting in a top-loading washing machine, fill with water, stop the machine, hand push down on the batting until it is soaked through, move to spin cycle to spin out water, then dry in a dryer.
Important to understand, however, that not all cotton batts can be pre-washed. For example, Mountain Mist Blue Ribbon cotton batting is a truly traditional batting that is made without any bonding, needlepunching, or scrim. Even soaking this batting will cause it to separate into horrible clumps. A batting like this will say on the packaging that it should not be pre-washed.