First off, don’t think to yourself that she would enjoy being able to see out of the container and would like to feel like it isn’t too small! Your brain will tell you that, but you denounce it for a liar!!
BOX: What you need is a pretty small box that is completely opaque. I would say a dark box. A small cardboard box would work fine. The goal is to have about an inch on each side of your turtle AFTER you put in the padding, so size appropriately.
PADDING: So I used sponges (link). Pro Tip, don’t use sponges with a scratchy pad size in case she tears through your padding and starts to burrow. Get a sponge that is soft, i.e. doesn’t dry to a hard lump. If you buy a sponge that is dehydrated, make sure you hydrate them and let them dry completely before using.
LINING: You can line it with paper towels, but they can tear through them. I think microfiber towels would also work.
LEAVE THEM ALONE: Don’t check on them constantly through the drive. Depending on how far you are driving, maybe check on them once in the middle. The goal is to put them into a dark, cave-like environment and leave them alone. Opening the top will stress them out. If you use a cardboard box, poke holes in the top and don’t fold the tops together. Fasten the top down with rubber bands, something easy to undo and redo to check on them.
DON’T STRESS: Finally, don’t stress too much. If there is anything I have learned about having a turtle, it is that they are super hardy and mostly attempts on your part to over-clean the tank or check on them too much will just stress them out.