An investigation is presented of the role which trapped particles might play in the driftwave stability of the ELMO Bumpy Torus (EBT). The model adopted consists of a bounce-averaged driftkinetic equation with a Krook collision operator. Care has been taken to model, at least in an elementary way, the features which distinguish the physics of EBT from that of tokamaks, namely the large magnitude and velocity-space dependence of the poloidal drift frequency Ω, the relatively small collisionality ν / Ω, the enhancement of νeff for passing particles, and the closed nature of the field lines. Instabilities are found which have a somewhat dissipative character; however, the precessional drift is found to be a significant stabilizing influence. In most cases the modes are completely stabilized when ω*/ ℓΩ ⪅ 1 for normal gradients. For reversed gradients (ω*/ ℓΩ < 0), stability is greatly enhanced.