What type of account is bills payable account?

ALL payable accounts are liabilities no matter what they are for. Whether it is a bill payable, mortgage payable, note payable, wages payable, etc, they are all listed as a liability.

This is because a "payable" is something you (your company) owes but has not paid yet. For a bill such as Phone, once the obligation is met it is no longer a liability but an expense.