What does bondable mean on an application form?

It means that a bonding agency would be willing to carry a bond to guarantee your behavior. Typically, if you have been pretty honest and don't have any felony convictions or bankruptcy, you'll be bondable. What is being asked here is essentially whether or not you will pass the background check. If you are free of criminal activity in your past, you will be bonded to the company, so that in the event you steal or commit fraud against them, the company is covered for the losses you have incurred. It is asking if you are eligible for a Bond, often called a Fidelity Bond. It is an assurance that you are free from criminal activity and that the comapny will not incur loss if you do come to work for them and steal or commit a fraudulent act while employed.