Largely due to its geometry-endowed bistability, the origami waterbomb base offers wide-ranging engineering potential. Here, we explore how nonzero crease curvature, which leads to panel bending, enhances the tunability of this structure. To reveal the influence of crease curvature on the deployed geometry and the mechanical response of the octagonal curved-crease waterbomb base, we combine physical experiments with a parametric numerical study. The crease curvature ranges from zero (i.e. the well-known straight-crease waterbomb base) to the maximum curvature possible within the allotted boundary. In addition, we perform finite element analysis (FEA), which incorporates crease plasticity and also allows us to examine the effects of crease stiffness and sheet thickness on mechanical behavior. Our results show that increasing crease curvature reduces the folded height and vertex range-of-motion, but raises the critical load for snap-through instability, without necessarily increasing the switching energy. Applications for these tunable structures can range from small-scale, energy harvesting mechanical metamaterials, to architectural scale adaptive shading devices and large-scale deployable space-based solar power systems.