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Proton therapy presents an interesting and important challenge to accelerator physics. Practical restrictions such as room size, gantry weight, and cost have led to a demand for more compact and affordable devices. Success would benefit a significant number of patients every year. Dielectric wall accelerators could provide this breakthrough, but there is limited work available regarding their feasibility or possible integration into medical devices, and no solutions exist for longitudinal beam control. In this work, we discuss the development of a linear beam dynamics model for dielectric wall accelerators. The model is implemented as part of the open-source code transoptr. It is tested against the rf LINAC subroutine in transoptr and is used to study bunch injection and transport. Building on recent work, the effect of time-varying fields on beam dynamics is also investigated. Conditions for limiting transverse beam size and maintaining longitudinal stability are discussed, and considerations are given to accelerator and beamline design.