Axisymmetric radial Bernstein modes are known to exist in non-neutral plasmas and have been studied theoretically and computationally in 1D, but detection of these modes has still proven to be difficult due to self-shielding. To help advance the work on this front we created a 2D particle-in-cell (PIC) code that simulates a non-neutral plasma in a Malmberg-Penning trap. A detailed description of the PIC code itself has been included that highlights the benefits of using an $r^2$--$z$ grid and how it can be tested. The focus of the PIC simulation was to discover how best to drive and detect these modes. While it is improbable that radial Bernstein modes will be detected in long plasmas, we show that it may be a possible due to the axial nodal structure in the potential and electric field generated by confining plasmas of any finite-length. Additionally, we find that for a short plasma the strongest detection signal along the trap wall occurs at the plasma's midpoint rather than near the ends. Results show that oscillating the confinement potentials is sufficient to excite the fundamental radial Bernstein mode, but not any of the higher order modes. The higher order modes can be seen in the simulation, however, by sinusoidally driving the radial electric field. Unfortunately, the individual modes are difficult to isolate which we suspect is due to mode mixing. Finally, we report frequencies and mode shapes for the fundamental mode and the (lower) first higher order mode.