Hi, rprice

There is a way to set up payments from your bank to the vendor's bank.

You can find information for that process here:  http://support.qbo.intuit.com/support/answers.cfm?faq_id=5374
A few other facts that may help: 
Who needs to sign up at Intuit PaymentNetwork? Me, my vendor, or both of us? 
Both of you. Signing up for an Intuit PaymentNetwork account is free. Your vendor pays nothing to accept your payment. 

What if my vendor doesn't have an Intuit PaymentNetwork account? 
If your vendor hasn't signed up for the Intuit PaymentNetwork, you can still try sending your payment. We'll email your vendor and let them know that they've received a payment. They'll be notified they need to create a free Intuit PaymentNetwork account in order to get your funds deposited to their bank account. If your vendor chooses not to create an Intuit PaymentNetwork account within 14 days of your payment, we'll refund your bank account with your payment. 

I'm not sure if some of my large vendors will be checking their emails for payments. Should I still try to pay them via Intuit PaymentNetwork? 
We recommend that you do not try to pay these vendors via Intuit PaymentNetwork. Intuit PaymentNetwork works best for those small and medium-sized vendors that you can contact by email. 

How does PaymentNetwork record a vendor payment in QuickBooks Online? 
When you pay a vendor using Intuit PaymentNetwork, your QuickBooks Online records update automatically. You'll see 2 new transactions: 
A bill payment transaction that comes from the account you specified when you made the payment. 
A check transaction that records the 50 cent processing fee. This fee is recorded against the expense account you specified when you made the payment. 

That is the process available for ACH payments integrated with QuickBooks Online.