My understanding would be that bonded means the birds
consider themselves a bonded pair, meaning they mate and
maybe have had eggs together. They may or may not have ever
actually produced any chicks. Proven means a pair that has
actually produced, hatched and raised chicks. If you are
thinking of buying a pair, be very careful. The terms can be
used pretty loosely when someone is trying to make a buck.
If they are claiming "proven", the question to me would
always be, how do you prove it to me?