In the end bite (more probably a sore mouth) can be avoided by smoking technique, the biggest feature of which, and difficult to accomplish, is slow smoking. Most of us, including me, want to light the pipe and puff away at whatever pace we choose, mostly without concentration. No, wrong, the best pace is to keep the tobacco smoldering, just above going out. Most mouth irritation is due to puffing hot smoke into your mouth at a rate that irritates its tissues. And it is supposed fact that the lower the temperature at which tobacco combusts, the greater the flavor.
If one is smoking slowly he has to adjust to tasting the smoke at a much lower volume, but I think this is simply an adjustment to the tasting experience. The biggest impediment to my slow smoking is that in order to accomplish it, one has to have a continuous thread of concentration on managing the pipe rather than just enjoying it. Things pull me out of that concentration.
One of the best ways to smoke slowly is called breath smoking, and the video below, hosted by an older Irish gentleman, is one of the best I've seen, although GL Pease also has a write-up of what appears to be a more advanced version:
https://www.youtube.com/watch?v=0o8Sfg6EH9k
Tobaccos vary according to their potential for irritating one's mouth, straight VA most especially. But if one is in control of his smoking, as you would be if you mastered breath smoking as taught by this gentleman, one can remain beneath the threshold of his mouth's discomfort.