According to the firm, 72 per cent of investors did not buy stock in the 55 pence a share offer.
This means that the sale's underwriters, who include Citigroup and UBS, are left with around $540 million of unwanted stock.
The bank had launched the rights issue in a bid to shore up its balance sheet, which has been hammered by credit crunch related losses.
B&B said in a statement that there was "no material change" in the company's earnings outlook.
It added that its full-year forecasts remain "cautious", due to "difficult" market conditions.
B&B's rights issue has been markedly more successful than other share sales which have recently been launched by UK banks.
HBOS, Britain's second largest mortgage lender, sold just eight per cent of its shares earlier this year.