which bitcoin web wallet lets you transfer bitcoins to a bank account?
If you are in the Philippines coins.ph would be the best,
It has plenty of cash-out option that you could choose and my favorite is the card less where they will provide you some codes and that's what you are going to use to withdraw in some ATM machines.
Yes. Coins.ph is so versatile.
You can choose what option you wanted to use for your cashout. Ita either through your bank account or direct to some money exchanger. But you can't store huge amountof coins here as this is an exchange and online wallet at the same time. Try electrum, it best suited for me and I didnt encounter major problems so far.