I've heard of people with larger bikes (esp. Goldwings) loading their gear onto their bikes, and have also heard of people using trailers, although I don't know anyone personally who does this.
I ride my motorcycle to the dive shop frequently, but not to dive sites, because I don't think I could safely load all the gear I need to bring onto my motorcycle. Of course I have a lot of gear due to the cold water, and my bike isn't that big (Suzuki GS500E.)
However, I have sometimes ridden my motorcycle to the pool to help with OW classes, because the tank and weights are being carried in the dive shop's truck. If I lived someplace warm, and was going to board a dive boat that already had the tanks and weights, then I'd probably do the "ride&dive" a lot!
One other thing to think about when considering riding to your dive: Diving can be very tiring, and depending on your own size/strength compared to the size/weight of the bike, it might not be advisable to ride a large motorcycle loaded down with gear when you are tired out from your diving activities.