rans6andrew,
You can certainly do an awful lot of stuff remotely these days,anything from power cycling and changing BIOS settings upwards....
The "issue" we have here is that you want to do it over Bluetooth. Something which theoretically shouldn't be an impossibility, but you'll need a good dose of persistence. But since you're into writing and compiling C programs, I'm sure you're happy to troubleshoot .....
Perhaps, if you wanted to keep your life modestly simple, you would connect your bluetooth adapter to the serial port rather than USB port on your computer. I'm pretty sure getting console port over bluetooth to serial is quite a common application that shouldn't be rocket science to setup.
Console over USB is a bit different, although you'll probably need drivers and/or config work .... maybe something along the lines of what's hinted at here on the bottom post by "jojopi" ...
Raspberry Pi ? View topic - Console output on USB port (its a RaspberryPi thing I found on Google, but the concept is exactly the same for other Linux boxes will probably just need some tweaking). But I've never seen such a thing in action (spawning consoles on USB), so I can't vouch for the suggestions on that link .....