Let us start with, "When does the property become a REO?" A REO is a bank owned property, so if your placing offers directly to a bank or a bank's agent, then it's a REO.
Now let us tackle, "how do we find out the BPO from my broker/agent?" You will not find that information out, the bank isn't going to release their pricing strategy to anyone, they are trying to sell the home, not give it away. Chances are your agent doesn't even know the BPO unless they did it themselves. Banks get BPO's from agents whom they have relationships with in that particular community. They pay these agents to go out and complete the BPO for their benefit, not for the benefit of a prospective buyer. Just because it's a bank your dealing with, don't think for a second that they don't have some idea about what the home is worth in the condition it's in. Don't assume that they aren't going to act and behave like any other seller who is trying to make as much as possible in as short a time as possible. If you get a good deal, great, good for you however, just because it's a bank doesn't mean they are wanting to give the property away, they still need to cover cost and if possible, make some money, it is a bank after all.