I have a new client in a foreign country who wants to pay in advance by wire. Can I send an invoice that they can pay without seeing my bank information?

Welcome to the Community, @tom237.
 

We can sign up for QuickBooks Payments that accept payments from US banks that will let you send customer invoice and pay it online without your customer seeing your bank information, however, currently, paying an invoice online using a foreign bank in this service is unavailable.
 

In your case, I suggest checking or searching other third-party payment services that will help you send invoices and accept international online payments while keeping your bank information secure. To do this, you'll need to go in the Apps inside QBO.
 

Here's how:

1. Go to the Apps menu in the left navigation menu.
2. Click the Browse Category drop-down menu, select Data Sync.
3. Select the app you want to integrate.
4. Click Get App Now and complete the following on-screen instructions.

I've added some article that can help you record customer payments and how to use the Undeposited Funds account if the cash payments aren't deposited into your bank account yet:

Record invoice payment
Undeposited Funds account to record the payments in QuickBooks

Please let me know if you have other questions related with QuickBooks. Community Team is always here to help you.

@tom237 

Which foreign country? in Europe or another continent?

You can't use QB Payments to accept international payments. You can set up a virtual bank account as an escrow. I don't recommend sharing your primary bank account's routing and account numbers.