There are sites in the Philippines that allows you to do that, but is there anything like that in other countries?
In Europe we have
Cashila which works basically as a bitcoin "bank account".
You can deposit funds with bitcoin or euro and pay bills / send money to anyone in Europe. You can receive money from others as well - with bitcoin or euro.
It's a cool service and the only I know which has a banking license to do bitcoin to euro transfers.