The bank operates its own wallets, you transfer your Bitcoin to theirs (or just buy it from them.) Keeping the Bitcoin safe is their responsibility. If you want to spend the Bitcoin, you can transfer it back to your own wallet, or directly to the payee. You pay them some fee to do this.
Now, it has obvious downsides. Less privacy. Easier for the government to confiscate your Bitcoin. The bank could go bankrupt. But, a person might rationally reason that those possibilities are less likely than them stuffing up a wallet maintained by themselves. Especially if it was a major bank that they might reason is unlikely to go broke. Obviously the Bitcoin account would not be government insured so if the bank goes bankrupt you might lose it all.
If criminals break into your account and steal your Bitcoin – if it is due to a problem at your end, e.g. a key-logger on your machine, the bank shouldn't owe you anything. If it is because the bank screwed up, they should be liable to compensate you for the loss.