I used to clear the ash intermittently and tamp with a tamper, but for the last year have switched to tamping with my finger, clearing the ash only when the pipe is at one/third of the tobacco remaining, which means that most of the tobacco is gone and that whatever is left in the bowl is covered over with compacted ash from having smoked far into the bowl. If after clearing I can light what is left, I do so, but whatever life is left is usually short.
I stop smoking when I can no longer light what is left or what is left lights only a little and bites. Then I dump the bowl and clean the pipe. There is not much tobacco remaining at this point, and I don't taste anything nasty or bitter at any point during the smoke.
Any surgeon will tell you that although we all have the same basic anatomy, we are all physically constituted differently; pediatric anatomy reveals substantial dissimilarity. What follows from this irregularity, I feel, follows into our palate, how we taste and how we decide what we taste. Thus you may find tobacco bitter at different points during a bowl while I don't. Moreover, at the beginning of one's pipe smoking career there is so much information pouring through your palate deriving from the particular tobacco, the particular pipe, what you are tasting, what you have read that is retrievable about the blend as well as vague impressions from your day having nothing to do with pipesmoking but which struck you, that it becomes difficult to taste the smoke in the way that it is commonly held by those who've smoked longer, the "experts" and those who are said to write good, accurate reviews.
Which is to say that the early days of pipesmoking can be confusing and the ideas one gets during this time about pipesmoking highly subjective. The "cure" for this is more pipesmoking. It will clarify as you go.
Hope this helps.