Mmmmmmmh.....I think that there's no way to program a "true" bypass patch.
And then MP-1 has not a bypass function itself.
You could attempt to create a clean patch with solid state voicing and a completely flat eq (0 for bass, mids, treble and presence) and low values for OD1 and OD2..with the right amount of Master Gain to hear your sound coming out...but I don't know if the final result will 100% match your needings.
The best would be to use a FX unit with internal programmable loop (like the Boss GX-700 or the awesome Lexicon MPX G2) so that you could put the MP-1 in the loop and chain it through internal effects mix, activating the loop in those patches where you need the MP-1 only...I did this in the past with my previous MP-1 and a GX-700 and it perfectly worked.
The GP-8 is a too old unit to have an internal programmable FX loop, if I don't remember wrong...
Before buying my TC GMaj, I attempted to use my MP-1 within one of the programmable loops of a Zoom 9150 (it has 2 loops), but the result was actually crappy and I gave up.
In your case, I assume the solution would be a MIDI looper.