The ideal thing to use for a positive displacement supercharger bypass is an external turbocharger wastegate. This should be mounted so it bypasses the flow directly around the supercharger when open. It does not need to be very large. Try to imagine how much boost pressure you would lose if you drilled a one inch hole in your supercharger pipework!
It absolutely must be mounted so it flows in the correct direction. That is, increasing boost pressure would try to force the poppet valve off its seat.
Now most if not all external wastegates have two pressure inlet ports, one above and one below the control diaphragm. And the internal wastegate spring always holds the wastegate shut.
The trick here is to connect two control air lines, between the wastegate to directly across the throttle body. The idea here, is that the wastegate diaphragm senses the pressure drop across the throttle body, and increasing plenum vacuum opens the wastegate against the internal spring.
It should be obvious that at wide open throttle, the wastegate diaphragm sees zero differential pressure, no matter how high the boost pressure rises. That is the secret.... The air bypass is load sensitive and depends more on the combination of airflow, load, and throttle position, and not so much on just raw manifold air pressure.
At engine idle there will be sufficient vacuum to snap the wastegate wide open. The supercharger bypass will completely unload the supercharger at engine idle.
At light throttle constant vehicle speed there should still be enough vacuum to hold the bypass open far enough so there is zero measurable boost upstream of the throttle.
A little bit more throttle, and the wastegate closes slightly further and boost may just rise slightly. More throttle still and the wastegate fully closes, giving full available boost pressure. it is all wonderfully smooth and progressive in action.
Same when you lift off, the wastegate opens. For a more violent type of throttle movement, the wasteagate slams shut instantly at full throttle, and springs instantly wide open on throttle opening, as in gear changing.
Any boost spikes up stream of the throttle force the wastegate off its seat, so it acts as an over pressure relief valve.
Getting it working properly depends entirely on fitting a suitable spring to the wastegate, and that requires a great deal of thought and attention to get right.
The first requirement is that the spring be stiff enough to hold the wastegate closed against full boost pressure without leakage. But it also has to be weak enough to open the wastegate against plenum vacuum at part throttle.
The problem is the ratio between poppet valve area and control diaphragm area. A ratio of at least 2 x diameter (4 x area) would be a minimum requirement, and many cheaper wastegates do not have sufficient difference in areas to work properly in this application.
But you can work all this out for yourselves. You may wish to be able to drive around with the supercharger unloaded with plenum vacuum higher than perhaps 5 inches Hg. That is 2.5 psi (roughly) But it must also seal against say? 10 psi of boost. You can see that if the two area have only a four to one ratio, it might be very difficult trying to juggle a spring that can achieve both these requirements.
So try very hard to find yourself a wastegate with a huge diaphragm diameter, and a reasonaby small poppet valve flow diameter. The Chinese gates with the crap diecast bodies and nasty low temperature rubber diaphragms work fine in this application, provided the area ratios are sufficient. And that can take some searching. The more expensive "brand name" Japanese gates are mostly excellent, but far from cheap, not all meet the area ratio requirement so be careful.
It may be possible to build a "Frankenstein" hybrid wastegate by mixing parts, to get a higher than standard area ratio. The larger the ratio, the less critical spring selection will be.
While setting all this up, drive around with the wastegate on the passenger seat or floor, and watch what it does. It will respond instantly and progressively to throttle opening, just like the needle on a vacuum gauge does. Get the spring sorted, then install it onto the engine. I think you will be extremely pleased with the results.
This system works equally well on supercharged or twincharged engines. I have been fitting this to street vehicles for well over eleven years now, with great success, and others that have copied it are also very pleased with the results.
Sorry for the barrage of words. It is really a very simple idea, just difficult to express in very few words.