Normal big paint bucket? Normal big trash bucket? See the problem? Just a ball park for outer dimensions would be helpful. I've seen people say they put a "bucket" in and it turned out to be a small flower pot.
And, again, does she have easy access to the bin? Can she climb directly down into it or does she have to go to the bottom, then climb up into it?
Unless you're watching 24/7, she probably does move much more than you think. Mine play statue when I walk in, and if they are out of their normal positions when I walk in, they return to "normal" in this super slow motion, bionic chameleon sort of way that just cracks me up. But, based on where I find poop and where I see the plant eaten, I know they travel.
They are "territorial" animals and seem to pick one area to be "home base"....they'll go away from home base, come back, head out in another direction, go back home, etc... so to us, it tends to look like they are always very close to the same place.