Ok to refuse. If the thyroid nodule is stable like you said, there is no need for a repeat biopsy (unless the last one didn't get enough materials or if your doctor was concerned about something with the last biopsy). Discuss this thoroughly with your physician. As long as you continue to follow the nodule, you will be able to intervene sooner if something changes.
Very Low Risk. If you have already had needle biopsy, or fna, done and it was benign, it's ok to just follow thyroid nodules on us. However, if no needle test done, it really should be. Thyroid cancers can grow slowly over many years, and failure to enlarge significantly on us does not prove a nodule is not cancer, especially if < 1 year between uss. Biopsy is very low risk, and should be done.