Does Bathurst have four distinct seasons

Not really,

Autumn is over in the blink of an eye unfortunately. Pretty sunsets but it's time to bring your wine/beer/bbq inside as soon as that sun goes down because it's going to get very cold. Most of autumn in really just a part of winter.

Winter is winter, a real winter! One that will make you hibernate for 6 months and come out the other side wondering what you actually used to do when it was warm. If you love being cold then you will love Bathurst. Most people don't embrace it though, they hide inside.

Spring and summer are great. The thunderstorms in November to mid December are quite reliable. The rain is reasonably reliable.

The only time that Summer is bad in Bathurst is in drought, the drought of 2019 to February 2020 was horrible and the town got down to 28% water capacity in Ben Chifley dam. Water restrictions meant that every lawn was dead (even in the new housing developments where the owner had just spent $6k on turf, although there was some leniency).

If you have moved from a temperate area by the coast or a lower elevation and you are a gardener:

Prepare for an entirely different form of gardening. Expect a lot of seedling losses in vegies, flowers and even natives. Frosts can come out of the blue and kill plants. Chillis don't do well and will die off and not come back the next year etc.