The best environment for any fish is one that closely matches its natural home. Unfortunately it is rather challenging to provide that kind of environment in a vase. However its not impossible make the vase a reasonable home for your Betta if you are willing to make the effort. You haven't mentioned what part of the country you live in. In climates that are warm year round a Betta can do pretty well in a vase; provided the owner changes the water regularly, keeps the vase clean, and provides the proper diet.
Is Warm Water Needed for the Betta?:
If you live in a northern climate, wintertime can present obstacles. Cold temperatures won't necessarily kill the fish outright. However, being subjected to long periods of cooler than optimal water temperature will stress the fish, rendering it far more susceptible to disease. Placing the vase in a warmer location in the house will help, but the best option for those living in cold climates is to keep the fish in a heated aquarium.
Another option is to put a mini-heater in your vase. Keep in mind that bowls are challenging when it comes to maintaining the proper temperature. It is easy to over heat, underheat, or have wide variances in temperatures. Frequent large temperature swings can be as stressful as constantly low temperatures. If you choose to keep your Betta in a small vase and heat it with a mini-heater, make sure you monitor the temperature closely.
Does a Betta need a Plant to Eat?:
As for a plant, don't add a large plant to the vase. Although some report that Bettas will nibble on a plant for food, that is not entirely true. Bettas require meaty foods and are not plant eaters in nature. Yes, if they have no other food available, they will nibble on the plants. However, plant matter is not the ideal food for them.
Furthermore, it will be much easier to care for your Betta if don't have a large plant in the way. If the vase is large enough, a small live plant can be used, but make sure the plant doesn't block out the entire surface of the water. Bettas need to reach the surface regularly. Do not use live plants in a vase that has only marbles for the substrate, as there will not be enough nutrients to support healthy live plant growth. A small in small pot of substrate avalible in pet stores will suffice, and be easy to remove when doing routine maintenance.