Dont't you have some kind of insurance for funerals in your country? I pay for life insurance and it also cover the funeral costs, but there's also plans where you pay a fee monthly directly to the "funeral home" (i dont know if this is the right word), and it cover the costs when you die.
About saving money on a bank account, you should give a look for the laws in your country, using my country has a example (Brasil), when someone dies, a lawyer must gather information about every asset (and this includes money in the bank) the person left, to determine how the inheritance will be distributed. So the money won't be readily available to pay the funeral.