Duckweed is common and usually available, but you have to be careful, depending on what kind of filter you have... an output of a hang-on or cannister could blow the stuff all over the place. If you just have a little sponge filter, it would be ok.
Better would be Ceratopteris Thalictroides (Water Sprite), also pretty common. It can be floated or planted. The nice thing about this is it is larger and the roots grow down, too, so the betta can swim amongst those. I just recently put in some smaller baby sprite in my betta tank and I think the bettas like it better than the salvinia natans (like a large duckweed). It sure is easier to deal with at water changes.