Exactly right - it's a cost to the business (not the individual) so putting the expense on Schedule C is proper. I have always included UBT (and another NYC local business tax, the MCMT) on the Schedule C line "Taxes and Licenses".
Note that while the IRS allows you to count these local taxes as a cost to the business, NYS wants you to be more specific about how you claim them. So early in the process of doing the NYS return in TurboTax, there's a place to add those numbers back in. Then, when you get deeper in the NYS return, you enter in the estimated amounts paid, and you get the credit.
