My taxes are done with the exception of efiling them. Is there a way I can find out how much my TurboTax bill is going to be?

Check your fees this way:

Open your return ("Take me to my return"), then click in the left menu column on TAX TOOLS, then TOOLS.
In the Tools window choose MY FEES.

You appear to be using Premier (at least that is what is indicated by your screen name above).  A Premier Federal return is currently 59.99, and a State return is 36.99.

If you pay upfront with credit/debit card or a prepaid debit card you can buy in a store, you can avoid an extra service fee.
If you choose to pay out of the Federal refund, there is an additional 39.99 service fee (44.99 for California filers where it is bundled with Premium Services.)    If you already chose that payment method, we can tell you the proper way to remove it and pay upfront.

NOTE:  Prices will increase if not filed or paid in advance by the end of 2/28.  After 2/28 Premier will then be 79.99 for Federal and 39.99 for State.