I have been a bonded employee a few times. For a courier job and as a home health worker. In both cases my employer did a criminal check to ensure I had no criminal record.
As I was dealing with legal documents in the one case, and being inside someone's home in the other these employers do not hire people with criminal records. I assumed being bonded meant my records had been checked and my employer was guaranteeing that I was trust worthy and did not have a criminal past.
That's my understanding anyway.
i think this is the correct answer