The old socks in your sock drawer have but one purpose: to hold the new ones you wear up where you can find them.
Backing also has a main use: to hold your fly line up to where it's near the rim and you can retrieve line at a decent rate, and to not have it coil due to a small storage diameter.

Bass are not known for long runs like bonefish or permit. Trout run a lot more, and I haven't seen my backing more than once or twice in the last 10 years. And then usually on tail-hooked fish in a current.
I'd say get the largest size backing you can find (30#; 50# is hard to find) and put just enough on the reel to bring the fly line to the rim, or near it. That takes less backing using a larger diameter, and 100 yds of 30# costs about what 100 yds of 20# does. Your reel's manual should tell you how much that will be.