We also have a basset!
They tend to have several things that can cause stinkiness... first check her ears, next check her feet (in between her toes), both places can get infected and can get yeast infections. Lastly, and this is pretty gross, check her bottom. Bassets are prone to build up in their anal glands which can smell REALLY bad. She might have to have her anal glands expressed by your vet. Our dog has to have this done every 2 months or so.
If the odor is just the regular "dog smell," maybe try taking her to a groomer once every 1-2 months. I'm not sure where you live, but we take our dog to Groomingdales, it's at about 77th & Quivira in Shawnee, and usually costs about $25-30. They are great, she LOVES going there and always comes home smelling fresh & clean.