Risks of developing second-hand cancers from radioactive iodine are extremely small. Remember, this is not a new treatment for hyperthyroidism or thyroid cancer. It has been used widely for more than 50 years.
With very high doses, patients can develop leukemia, but that is more than patients get, especially for hyperthyroidism (you get more for thyroid cancer, since they want to destroy all the thyroid, not just part of it).
There has been some research that suggests that there is a small increase in other cancers, including bladder cancer, after treatment. However, these were thyroid cancer patients and they may have already been at higher risk for secondary tumors. Do a search for "radioactive iodine and bladder cancer" and you should see a few results.
I think that working around nuclear weapons would be more likely to cause your bladder cancer than the radioactive iodine would.
I hope the cancer is in an early stage and is treatable. Good luck.