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!

It depends on the context...although my first impression is "something that must have the ability to be stuck onto something [with glue]". It's difficult, because the word 'bond' has many meanings in English; a) to stick together b) something that joins two things physically c) a loan to the government paid for by private citizens d) the relationship between two people

A bond in this sense is defined as: An insurance contract in which an agency guarantees payment to an employer in the event of unforeseen financial loss through the actions of an employee. For a person to be bondable means that they don't have any criminal or civil record that would cause the agency to deny such a contract covering the person.