I currently have to have my iPhone physically connected by USB to run remote debugging in Safari. Is it possible to do it via bluetooth or some other wireless method?
You have to plug the phone to your computer, is not possible to do it remotely so far.
It is possible now - I put it here to tie the threads - see here
https://apple.stackexchange.com/a/333876/100894
It is now possible to do wireless remote debugging using "Safari Technology Preview":
Remote debugging with mobile Safari also works without a cable connection to the desktop computer. But you have to install Safari Technology Preview on your Mac as the stable Safari version currently does not support wireless remote debugging. Just do the same setup as described above, but connect the cable and open Safari on your iOS device. In Safari Technology Preview, make sure you enabled “Show Develop menu in menu bar” and enable Develop → "Your mobile Device Name" → Connect via Network in the menu. Now you can unplug the cable and check whether Develop → "Your mobile Device Name" still shows up on the desktop Safari.