The Mice Muon Beamline and Host Accelerator Beam Bump The international Muon Ionization Cooling Experiment (MICE) is designed to provide a proof of principle of the technique of ionization cooling, the reduction of the phase space of a muon beam exploiting ionization energy loss in absorbers. Subsequent re-acceleration is then provided by RF cavities ("sustainable cooling"). Ionization cooling represents an important step toward future facilities based on stored muons beams, such as a future Neutrino Factory or Muon Collider. The MICE Muon Beam begins with the decay of pions produced by a cylindrical titanium target dipped into the circulating proton beam of the 800 MeV ISIS synchrotron at the Rutherford Appleton Laboratory, U.K. This generates a pion shower which is captured and subsequently decays producing the muon beam. A secondary effect of the MICE target is to cause an increase in the number of protons lost from the ISIS beam, known as beam loss. An overview is presented here of the MICE Muon Beamline, including the results of a study of the effect of dynamically raising the vertical position of the ISIS beam (a 'beam bump'), in the vicinity of the MICE target.