Sometimes it happens that iPhone Bluetooth fail to connect. Follow the step below to fix the problem.
1. Go to Settings> Bluetooth> Tap on the apple pencil exclamation mark icon
2. Click This Forget Device and a message will popup then click OK
3. Then reconnect the device again - by toggle on/off on the swipe up page.
4. Do a hard reset by pressing on the Sleep/Wake button and Home button at the same time and then wait for it to restart
5. Once restarted swipe up again to bring up the panels and toggle on/off the Bluetooth
6. Now test to pair with other Bluetooth devices to check if the problem fixed
7. If still doesn't work try to Update the software by Settings>General>Software Update
8. Once update is completed - then perform network reset by Settings>General>Reset
9. Tap on Reset Network Settings and then try turn on Bluetooth to pair with other devices again once it is completed