iPhone 11 issues - unable to connect to Bluetooth or download iOS 13.1

Hello and welcome to Apple Support Communities ChristieMK,

If I'm understanding you right, you're unable to connect to any Bluetooth devices on your new iPhone 11. Also, you've been unable to update the iOS version as well. I know it can be pretty distressing to experience issues with a brand-new device. I'm happy to give you some steps to try to see if this can be resolved.

Since updating your iOS version is a very important step for the Bluetooth issue, I recommending starting with that first. Steps to resolve the exact error message you're receiving when you try to update are outlined in Get help with over-the-air iOS updates, specifically these two sections:

"If you can’t reach the update server or can’t verify the update

If you try to update the iOS on your device, you might see one of these messages:

"Unable to Check for Update. An error occurred while checking for a software update."

"Unable to Verify Update. iOS failed verification because you are no longer connected to the Internet."

Try updating your device again using the same network. If you still see one of these messages, try updating your device using another network or update your device with iTunes. If the issue happens again after trying to update with multiple networks, remove the update.

Learn more about iOS updates.

Remove and download the iOS update again

If you still can't install the latest version of iOS, try downloading the update again:

1. Go to Settings > General > [Device name] Storage.
2. Find the iOS update in the list of apps.
3. Tap the iOS update, then tap Delete Update.
4. Go to Settings > General > Software Update and download the latest iOS update.

If you don’t see the update in the list of apps or if the issue happens again, you need to update your device with iTunes."

Once you've updated your iPhone to the most recent version available (iOS 13.1.1), test out Bluetooth. If the issue persists after updating, try these steps and test your Bluetooth after each one:

1. Toggle Bluetooth off and back on again. Make sure you're doing this in Settings > Bluetooth, and not from the Control Center.
2. Make sure your Bluetooth accessory is in pairing mode. If needed, check with the accessories documentation for help on how to do so.
3. Restart your accessory and your iPhone.
4. Verify the accessory you're trying to use is one that should be setup and paired in Settings > Bluetooth. This is important because some accessories may require being setup in third-party iOS apps.
5. Make sure your Bluetooth accessory has the latest firmware installed on it. Some accessories require firmware updates to work properly with new iOS versions.
6. If possible, reset your Bluetooth accessory to factory defaults. You may need to check the accessories documentation for help on this as well.
7. Rename your iPhone in Settings > General > About > name.

Thanks for using Apple Support Communities.

Take care.