Good advice from Kim.
Since you know the property address, have your Realtor run the comps on it. He or she will be able to go into the MLS and pull up the information from the last time it was sold--the complete listing and description. Admittedly, you don't know what the condition inside is. Assume it's below average--assume it's in worse shape than a conventional sale. Still, you can come pretty close to what its true value is.
BoA will have a BPO (like an appraisal) done on the property. However, BPOs often aren't accurate. If you're lucky, the BPO will be under what the real value is. What'll happen is that when the bank's ready to put it on the market, it'll likely price it around the BPO price. Then, if it doesn't sell at that price, it'll steadily reduce the price until it does sell.
Your number is: What is the house worth? Not the $242,250. First, it wasn't "given back to the bank." It was never the bank's to begin with. Second, that's not the full amount of the bank's expenses in the house. There are also legal fees, carrying costs, etc. Third, realistically, if the home was purchased in 2005 or 2006, it's likely that it was a 100% mortgage, and that values have declined since then. So, just a guess, the house is worth substantially less than $242,250, even though the bank's total investment in it may be up around $275,000.
The only thing you care about is: What is the house worth. That's it. Period. Then you make an offer at or below that figure.
Sounds like you got some decent advice from the broker who deals with the BoA properties. However, I'd strongly advise that you find your own agent. Someone with experience with foreclosures, but a buyer's agent who'll represent you. The broker you talked with will (if he gets the listing) have a fiduciary responsibility to BoA.
Hope that helps.