Hi Nohackme,
Mike is right about the train and bus. But it is closer to three hours, and you want to make sure you are on an earlier train in case the one you plan for is cancelled. There is a web site to help you plan your trip
Journey planner The destination you want is probably Delaney Ave/Point Nepean Rd,which is the last stop.
Unless you are bringing everything with you, please be aware that according to the Red Boats Web site they can arrange tanks, but do not hire gear.
FAQs Archive - RedBoats
You may be able hire kit from BayPlay at Portsea, but contact them to confirm. I have had no experience with them.
www.bayplay.com.au
Generally the closer to the CBD you get the murkier the water, and a good dump of rain will, make it worse.
The scuba doctor has some info on shore and pier dives.
Melbourne Dive Sites - The Scuba Doctor
You may want to think about hiring a car and driving down, but it will still take you around 90 minutes, but will give you more flexibility, there are a couple of dive shops that hire gear that you could get to, without going too far out of your way.
The water temperature inside and outside the bay is 16 C or just under 61 F, at the moment
Hope you enjoy your time in Melbourne