Don't worry about the bark unless it looks moldy, diseased, or houses a bunch of nasty bugs or something. Go ahead and smoke away!
The bitterness will come from the creation of creosote and not from bark. To minimize the potential of this, leave the outlet open and control your fire at the air intake. Also, make sure your wood is nice and seasoned. A lot of people take their dry wood and then soak it prior to adding to the firebox...you don't need to do this either, as the water penetrates very little, and only serves to delay smoking while the water boils off.
Here is a link to a discussion of wood...check out the video in the center of this...I thought it was informative.http://www.virtualweberbullet.com/woods.html