This usually refers to a candidate for a job. The employer wants to know that the candidate is low-risk. The employer will try to buy a bond from an insurance company that promises to compensate the employer if the candidate steals something from the company after being employed. The insurance company will do a background check of the employee candidate before issuing the bond. "To be bondable" means to be capable of passing the insurance company's background check so that the insurance company will issue the bond.
I might not have all the details and terminology exactly correct, but this is the general idea. I hope it helps!