Can I connect to a shell from a PC to my Android using bluetooth or USB? I want to run some commands on my rooted android phone. It is not very practical to interact with a shell using the touch screen, therefore I wanted to run a daemon on it and connect to it from a PC. I can't use the wifi connection for that because it is not working properly. I figured that it should be possible to do it via bluetooth or USB, but I could not find information on how to do it.

Is there any ready-to-use solution?
Yes, just use ADB over USB and run adb shell.  See http://developer.android.com/guide/developing/tools/adb.html#shellcommands