A number of benefits result from reducing the period length of an undulator without sacrificing magnetic field strength, such as an increased photon flux and higher energy synchrotron radiation. Replacing permanent magnets with bulk high-temperature superconductors (HTSs) has proved to be an effective path towards this goal. We present a concept for a bulk HTS undulator that is magnetized via pulsed field magnetization, which is a much more compact and economical form of magnetizing HTS bulks compared to the field-cooling or zero-field cooling methods that are typically employed. The results from an experiment tailored to demonstrate the feasibility of this concept are also presented. With these results, we estimate that an undulator field of 2.3 T could be generated using this design with a magnetic gap of 4 mm and a 16 mm period length, operating at 40 K.