WATER SPRITE!! I put that in caps because all of my bettas LOVE it. If you leave it floating, it provides them with cover at the surface. Two of my boys use it as their beds/loungers. One of them blew a bubble nest in it.
Java moss is another great plant for aquariums. It's very versatile and is very effective at keeping up water quality:
Sorry, I don't know which plants would be dangerous for bettas but I imagine that if you find one that you like, you would be sure to research it before adding it to the tank.