You are going to get (and have already gotten) a ton of responses, some of them conflicting.
My advice?
Do NOT clean out the bowl while breaking in your briar. It will take 10 to 20 smokes for it to be broken in. The cake should be about the thickness of a dime or nickel, and once it's established you will need to ream it every now and then to keep the cake to the thickness. Do NOT be overly fussy about this -- just ream it when it starts to get thick enough to be bothersome while loading.
You should run a couple of pipe cleaners through the stem after every smoke, and sometimes even during the smoke. The bitterness could be caused by all kinds of things. Just cleaning the stem regularly should help it out. You do NOT need to thoroughly clean your bowl after every smoke, although some guys insist on doing it (I imagine that would hurt the build-up of cake anyhow). I've got dozens of briars and have been smoking for 20 years, and have never had a bowl burn out or go "sour" or rotten or whatever. Every few months, it's a good idea to thoroughly clean the bowl with alcohol (I use rum), which help keep it sweet and fresh. If it's tasting bitter or nasty, you might need to let it rest for 2 to 3 days. Some guys will tell you it needs to rest after every single smoke (smoke once a day, basically, and then let it lie empty for several days). I disagree. I smoke my briars multiple times a day without problems and then let them rest for a couple of days, which is how most smokers did it in the era of our fathers/grandfathers. You can get by with a rotation of only three briars, or just use cobs to fill in the rotation.
Anyhow, to sum up: Clean regularly with pipe cleaners. Once it's broken in, clean the interior of the bowl with alcohol every few weeks, and let it rest for at least 2 days after every day of use. That should really help with this kind of thing.
You're going to get all kinds of advice here. Take notes, and try whatever seems to make the most sense. I really wouldn't worry too much about it, though. Your briar is not a Ferrari or some high-performance machine that needs an oil change every five hundred miles! It is a TOUGH piece of briar wood that is designed to take punishment. Briar pipes aren't invulnerable, and you do need to keep them clean, but they aren't in any way fragile.