In most cases, once you are identified as a match, you become part of the treatment and all your costs will be picked up by the patient’s insurance or whoever is paying for the transplant. Check with the transplant team to confirm your status regarding donor costs.
The initial testing cost is not covered by insurance, as it is considered elective; finding a positive match is very difficult and insurance companies generally are unwilling to pay for it.
As a potential donor you will receive a physical and a complete medical screening to ensure that you can donate safely. And, medical personnel will determine whether you have any communicable conditions that could harm the patient. Only after this screening will you be deemed a match.