Probably. If you're getting little swipes of trub from primary to bourbon barrel, then again to bottling bucket. It should have enough yeast in suspension to carbonate. My bet is you're not letting it condition long enough in the bottle. It also helps to let the bottles condition in a dark, room temperature location. I use the top shelf of a clothes closet in a spare bedroom and that works pretty well.
Beer so good, it's frightening.
2014: Seven Heavens Series One: Vilon, Mystic Melomel, Skeeter Pee.