Why do the payable bills and interest payable not come under provision account?

Thats because the provision is an estimate made under the prudence concept for a probable or expected loss against any recievable or asset, while Payable bills are expenses that have been accrued and are not probable but confirmed so its not an estimate when u have certainity about some expense also the benefit against it has been obtained 

Provisons are made when the accurate amount of liabilities can not be ascertained. Once it is established it will be expressed under as accrued. And payable bills (assumed as creditors for goods) are called sundry creditors or otherwise as a line item "Bills Payable"

provision account is account set aside in case of any liability

Provisions are not actual expenses whereas payables are actual expenses

Because they are accrued expenses.