How do you store a glass mixing bowls to prevent any scratches in limited space?

I use old tea towels.

I also use paper towel and paper napkins in a pinch, all of which will eventually end up in the compost bin at some point.

For regular use, it's worth cutting up swatches of old fabric. The Japanese frequently use linen for storing better pieces but feel free to use old t-shirts, pillowcases, sheets, etc.

I've used bubble wrap sheets as well when I know I will be rinsing out the receptacle before use.

I suppose one could use newspaper but I don't see the point when there are better things available in a typical home.

Irina - when I have anything like that I want to protect, I line the pieces with one of :
* clean paper towels (which I eventually use for their original purpose)
* clean dish towels (for larger items).