How large is the tank? 10 Gallons? If so, you should be alright if you do a good clean before you leave, with just one betta in it. If it's not being fed, or is only fed once or twice, there won't be much waste in there to cause problems.
Here's my idea: bettas are omnivores, so they will munch on plants. You should get a nice soft, tasty plant that your betta can chew on (not something thick and waxy like java fern). Get a bunch of plants in there, and then don't have the betta fed while you are gone. Bettas can't survive for the long term on just plants, as they are meant to have meat in their diet, but they'll be perfectly fine for a week. The plants will help absorb the pollutants in the water and your betta will have something to snack on, but won't be creating too much waste.