I haven't felt a need to cover my bag. However, when it is really hot, it sometimes wants to cling to my skin. A newborn baby bib has worked well for me. Just tie it around. I don't like the ones with velcro.
Also, the soft baby washcolths that are two layers work also. I cut a slit and put the bag between the two layers. It is very soft, comfortable, and doesn't add much bulk.
Both protect my skin from the heat. I haven't felt a need to beautify the bag.
I am sure there will be lots more options presented.