If you don't invoice the customer for your services, but have set up an
agreement to take a draw from the customer's bank, you still need to enter
an invoice so that QuickBooks can record the money you receive as income.
Create an invoice
from the estimate (and make adjustments, as needed), but
clear the To be printed checkbox on the invoice form. If you simply
deposit the money into your checking account, QuickBooks does not account for
the money as income.
When you get the bank draw,
record the payment in QuickBooks.