Not to sound like an A$$, but he probably did you a favor, if you cut the cape wrong and it was not long enough, if he would have stretched it to meet the size of the bears head you would have had that, a bears head, he might have put it on a smaller form for you to get some of the shoulder back for you. You can't have both width and length if you are lacking one of them in the first place.
As for stretching and soaking a cape, he has to do that, there is no way to mount a hide other than doing that, that is not a step that can be left out. Did you address this with your taxidermist when you picked it up?
But to answer your question corner of the eye to the corner of the eye, to get width between the eyes, the tip of nose to corner of the eye to get the length of the snout. Other than that there is not a lot of other measurements to take. There are only a certain range of forms out there, you can build one of them up. But not going to be exact.