Not he usual sort of chief dust masks (they may catch a lot, but not all). Hepafilter N95 masks are probably sufficient- at least they are good for tuberculosis mycobacteria, which are roughly the same size. Also, the spores are probably NOT pure cultures- they are mixed with some carrier powder (Lactose? Cornstarch?)for disemination. The carrier powder is relatively easy to filter out.
BUT (and this is a BIG "but") unless you are wearing the mask at the time of exposure, and you carry out careful personal hygiene (especially handwashing!), there is really no point in bothering to buy any sort of mask.