Vendors from my desktop version of QB Online don't show in the mobile version but when I try to add them, I get a message that they already exist. How do I access them?

Let me give possible information that you might miss out on, @lauren59.

The QuickBooks Online mobile app is always in sync with the web version. The tasks and changes you've made in the app should show up on the web and vice versa. 

Furthermore, we can check if the vendors are marked inactive. If they are not, we can reset the data in your mobile app.

Here’s how:

iOS

1. Go to Menu ☰ and tap Help & Feedback.
2. Tap Refresh Data. 
3. A message will appear that says, "Caution. If there was a problem getting your latest QuickBooks Online data, you can refresh it now. It may take a few minutes". 
4. Tap Refresh to confirm.

Android

1. Go to Menu ☰ then tap More Options ⋮.
2. Tap Settings then Refresh Data.
3. Tap YES to confirm.

Once done, you can close and reopen the mobile app and check for the vendors. Also, I suggest restarting your phone. If you continue to get the same result, uninstall and reinstall the application to start fresh. 

In addition, I've included this article for your reference if you want to learn how to keep your accounts, customers, and vendors organized: Merge duplicate accounts, customers, and vendors in QuickBooks Online.

I'll keep the thread open if you need additional assistance managing your vendors in QuickBooks Online. Click the Reply button, and I'd be glad to assist. Have a nice day ahead.