If you've got (or are willing to get) a pothos, just clip a leaf once a week or so and float it in the tank. The natural 'v' shape of the leaf provides a spot on top of the leaf for a betta to climb onto as a sleeping platform or, for those who prefer being under things, a bit of cover. A feeding clip can easily secure it to the side if you'd prefer to control where it is.
Cut it with as much stem as you can. This not only weighs down the leaf making it a better betta shelter, but also lets you clip the end every few days to keep the leaf fresh as long as possible.