Shock control bumps offer the potential to reduce wave drag on transonic aircraft wings. However, most studies to date have only considered unswept flow conditions, leaving uncertain their applicability to realistic finite swept wings. This paper uses a swept infinite-wing model as an intermediate step, and it presents a computational study of the design drag performance of three-dimensional bumps. A new geometric parameter, termed bump orientation, is introduced and found to be crucial to the performance under swept flows. Classic shock control bumps aligned approximately with the local to freestream flow direction can offer drag reductions comparable to those from similar but unoriented devices in unswept flows, whereas badly misaligned bumps see severe performance degradation. For appropriately aligned classic bumps, the relationships between performance and selected geometric parameters (height, streamwise position, and isolation) are found to be somewhat similar to those observed in unswept studies.