Yes, air purifiers do work for bushfire smoke. Most air purifiers are rated to deal with pollutants and particulate matter as small as .3 microns, while bushfire smoke particles tend to be somewhere between .4 and .7 microns. This means that most HEPA filters are going to be able to easily trap the matter that makes up the smoke, though there is no filter of any type that will be able to perfectly filter out sustained smoke over a lengthy period of time. If you have no choice but to be in the path of the smoke, a filter might be the best choice for your health.