Living here near Amish Country I have access to beautiful handmade baskets that I use in place of bags. They are so roomy and look so much nicer, especially when you use a vintage tea towel to cover up all the stuff. I feel just like little red riding hood with a basket of goodies! One problem though. The wood handles can be a little uncomfortable on the hands. No worries. I just made a super soft cover that keeps the hard edges from digging into my skin. Basically I made a large potholder, trimmed in bias tape and out of the cutest fabric! Then I sewed three buttons on the bottom edge and three button holes on the top. I mismatched the buttons for a fun accent.
I bet you could do the same thing with a purchase potholder! And if button holes scare you, (admit it, they can be frightening) just use some velcro instead.