Bayesian techniques have been shown to be extremely efficient in optimizing expensive to evaluate black box functions, in both computational (offline design) and physical (online experimental control) contexts. Optimizing physical systems often comes with extra challenges due to costs associated with changing parameters in real life experimentation, such as measurement location in physical space or mechanical/electrical actuation. In these cases, the cost of changing a given input parameter is often proportional to the magnitude of the change, for example the time cost associated with the distance a physical actuator must travel. To minimize these costs, optimization algorithms can simply limit the maximum distance travelled in input space during each step. However, hard restrictions on the travel distance inhibits global exploration advantages normally afforded by Bayesian optimization algorithms. In this work, we describe a proximal weighting term that can bias acquisition functions towards localized exploration, while still allowing for large travel distances if far away points are predicted to be valuable for observation. We describe a use case where this weighting is used to minimize the uncertainty of a particle accelerator Bayesian model in a smooth manner, which in turn, minimizes temporal costs associated with changing input parameters.