Also what temperature were you smoking at? If you are using too high of a temperature, and the fat is rendering, that is not ideal. Were you having a problem keeping the smoker at your set temperature?
It is best to try to prevent this problem. The more moisture the more smoke particles will absorb/adhere to the meat. This may cause a much stronger, more acrid smoke then desired. It may not be a major problem for the Bradley, since the burning of the bisquettes provide a much cleaner smoke. If you can't prevent this by widening the vent opening or adjusting your temperature, and it is a lot of buildup to the point you have to pour it off, at the end of the smoke; than blotting the areas with a paper towels, once or twice during the smoke could helpful.