There are two problems with that I can think of:

1. Bank transfers can be reversed in some circumstances (account was stolen etc). Some days after Bob gets the money and releases the bitcoins, the bank may reverse the transaction.

2. I'd be worried that the bank may freeze my account if I receive cash transfers from someone who turns out to be a criminal or the bank freaks out for some reason.

I would much prefer a centralized exchange.

This concept could work if A and B meet up and payment is made in cash. This concept could also work for trading between cryptocurrencies (btc <--> ltc etc)