As I understand, the "tunnel" connecting the tailpiece cavity and the electronics cavity in a Rick bass (don't know about the guitars) is used for the grounding, shielding or earthing (as it'd be in german, I don't know the proper english expression)? So the tailpiece should be connected to any of the potientometers with any kind of wire?

First, you are correct. In the USA, it's commonly called "grounding," and in the UK it's commonly called "earthing."

Usually, a wire connected to either the bridge base or tailpiece bracket is connected on the other end to either the common ground of the output jack or a tone potentiometer case, which is also grounded. The goal is to get everything to one point of grounding at the jack to eliminate "ground loops," which can exacerbate hum and noise.