On the cash basis, it would not count towards income. Since the cash was never received, there is no income. So not receiving the cash doesn't affect the P&L. Only receiving the cash does. The expenses are the expenses when incurred, regardless of whether you received the income associated with them or not.
On the accrual basis, the income is recognized when the service is completed and billed. In that case you have to count it as income, even if you haven't received the cash. You have to pay taxes on it, even though you don't receive the cash. That's the beauty of being on the cash method for most small businesses. You don't have to pay taxes unless you actually receive the cash. But, technically from an accounting standpoint, you can only have bad debt if you had income to begin with, so the bad debt account is only used when using the accrual basis.
To make a long story short, the term 'bad debt' has a very specific definition within accounting.
Of course, if you are aren't getting paid for work you have done, it still feels bad.