Apple - Can I control my Mac with my iPhone -- over Bluetooth?

I don't know of a general purpose Bluetooth only control that exists on the App store (but that store is really hard to search these days for a needle in the haystack of apps), but one of the more common remote control software packages does say it will work without WiFi on the Mac.

• http://www.airkeyboardapp.com/faq#no-wifi

Once you've installed the free Mac software and tested that you are OK tethering the Mac to the phone (which can use prodigious amounts of cellular data) you can download the free and ad supported iOS app.

• https://itunes.apple.com/us/app/air-keyboard-free-wireless/id541873446?mt=8

There is IAP to remove the ads if you really like it over time. I prefer to use the computer's create network and tether over USB if needed for control in situations where I don't have a pre-existing WiFi network. The apps I prefer for that are:

• Touchpad by Martian Craft - about $7 on the app store
• Rowmote Pro by Evan Schoenberg - about $5 on the app store

Touchpad is truly standalone, just turn on screen sharing on your Mac and run the app. Rowmote Pro is more integrated with various apps such as spottily, hulu, etc... Both function fabulously as a keyboard and mouse/trackpad for OS X from iOS and I find I use both for different tasks at different times.