Can there be a way of improving yellowing teeth without breaking the bank?

Try: You can try some of the over the counter whitening products or tooth pastes. Hydrogen peroxide may also help. Otherwise you will need to seek help from a dentist to discuss possible options.

Sure: You can try some of the otc products from your drugstore. They may not work as well as the professionally applied products, but you are paying less. Not sure what your budget is, but most offices can fabricate custom bleaching trays for $ 500, plus or minus.