In bumpy cylinder geometry, electrons are classified into trapped and passing particles. The interaction between a wave near the electron bounce frequency and the electrons is studied both numerically and analytically. It is shown that coupling of the waves to the electron bounce motion parallel to the magnetic field can lead to heating of those electrons near the passing/trapped boundary in velocity space. The stochastic threshold condition is eE0k0/m omega b2 approximately=0.1, which is an order lower than the quadratic magnetic well results. For this mechanism, the wave energy density required to induce stochastic heating in the ELMO Bumpy Torus (EBT) by radio frequency (in the frequency range of ion cyclotron resonance heating) is about an order of magnitude more than that estimated on the basis of cold plasma wave theory. However, it is suggested that the bounce resonance can enhance the electron cyclotron resonance heating efficiency in an EBT-like heating scheme.