Not a good idea. A vase is not a good home for a fish. Bettas are tropical fish and should have water temps 74F-82F. An vase of water in PA in the winter time can easily get to 65F in a heated home. These fish are marketed this way with the logic that the fish comes from stagnant waters, rice paddies and slow moving rivers so they are more than happy in a cup of water. The truth is even though the waters are somewhat shallow and murky they are complete eco-systems. A vase of water with a terrestrial plant in it isn't a good home for your fish. The colder water alone will make him lathargic and suseptible to disease and parasites. I know these fish are presented this way so its a little confusing, but a more ideal set up for your betta is a minimal 3 gallon aquarium,for a live plant a java fern is pretty and seems to do good almost anywhere. The live plant will help keep the water less toxic because it utilizes ammonia that the fish excretes. Its best to keep true aquatic plants with fish. Good luck. Maybe do a yahoo search on bettas in vases to see what others think or click the link below.

Here is a link that might be useful: Betta's in Vases

Swedish Ivy (Plectranthus australis) is non-toxic (at least to mammals)