How to account for bad debt
To settle the invoice to account for bad debt (either a full or partial loss of the invoice balance due to you), what I would do is record the payment for the money that you did get (if any) using the Receive Payment button on the invoice. This will reduce the balance due to the amount that you need to "write-off."
To write-off the balance, you can create an item called Bad Debt (or something similar). The easy way to do this would be to click New Item on a free line on the invoice, name the item, enter 0.00 for the sales amount since the amount will vary invoice to invoice and then choose the expense account that you use to track bad debt as the bookkeeping account. If you don't have an account for bad debt, then you'll want to create one and then come back and create the item. Save the item. Then on the line item for the bad debt enter in qty of 1 and the balance of the invoice due with a negative sign in front so that the system uses this to reduce to balance of the invoice. Your invoice balance should be at 0.00. Click Save and the invoice is now marked as paid in full so that it comes off your AR reports and the bad debt account is increased so you can use it to reduce your taxable income come tax time.
It is always best to consult your accountant/CPA when starting a new accounting practice to be sure it works for you and your state or industry regulations.