As far as I know the term "Bondable" means if you are "Insurable". If a Company/ Employer deals with finance, or some sort of money exchange etc. They need to protect themselves against fraud and/or theft from Employees. If a criminal act is traced back to an Employee who has committed a crime then the Employer is covered by Insurance for the amount that was stolen and could not be recovered.

As long as you do not have a criminal record or are a high-risk for criminal activities, then you are already Bondable, meaning you are Insurable. If you are red flagged or give off any warning signs that you are a high risk to the Employer or Insurance company then obviously you are not Bondable.

If an Employer is asking potential Employees if they are bondable usually means the company deals with money, such as Collection Agencies/ Call Centers, Banks etc. So they usually run a criminal record check and amazingly enough can even ask permission to run a credit history report