When I cook crumpets because the pan has to be so hot and the heat has to remain hot for the bubbles to form. How do I stop the bottom of the crumpets from burning?
The pan has to be hot, but this doesn't mean that it has to be the hottest setting you can get. There is a temperature at which you can get bubbles without burning them, you have to play around with the temperature until that happens.
Beside using the correct temperature - hot, but not unreasonably so - try getting a very smooth heat transfer. It works best with an iron pan. You should preheat it well, not at the highest temperature, but wait for a while at mid-high. An evenly heated iron pan will give all of your griddle cakes great surface without burning them, you only need the correct heat setting - quite high for crumpets and galettes, somewhat less for crepes, schmarrn and american pancakes. The worst thing you can use is an aluminum pan, I've never had good results in one of them despite their quick heat transfer. I suspect that they are just so heat conductive that their surface cools down when the cold dough hits them, so the major heat "border" is transferred just below the pan surface, instead of being just above the griddle cake surface, but I have no proof of that.
You can also try making them a bit thinner. A good strategy would be to make your dough somewhat wetter, so it will rise more in the pan, allowing you to have a somewhat thinner initial height for the same height in the end product. It will also make the crumpets somewhat softer.