Yes, that billowing white smoke is where you are getting the bitter taste. Creosote. It takes very little wood to impart the smokey flavor. There could be a few reasons so directing you to one or two solutions might not give you all the info you need, but we can sure cover few of them here.
Make sure the wood you are using is dry. If buying chunks or chips from a store, that usually isn't an issue.
If your using your own wood, a good sign that it is dry is the edges will be cracked.
Over use of wood can also leave a bitter taste, which goes back to a little wood goes a long ways.
When I first started, I too had this problem. Huge plumes of white smoke. I read about preburning my wood prior to adding to the fire, or in your case, the coals. Preburning is nothing more than, burning it, but not entirely. I will take a few pieces of wood and light them up until the outside is fairly well charred and it takes on a cracked surface. This helps in drying the wood even further and burning off and of the nasty things in there that turn into a gas form, which it what you are seeing in the billowing white smoke as they are being released. Some will also set their wood that they will use on top or even in the firebox, away from the flames and heat the wood up, almost to the point of ingition, but not quite. When you add the wood to the existing fire, the time it takes for the wood to ignite is almost zilch, and it ignites quickly.
Others will chime in here as well and offer some suggestions so be patient.
By the way, glad you found us. Always nice to have to members
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What type of smoker are you using?