in answer to the question in your original post - "yes" !
i am now in Koh Tao, the diving here is very good and there is a plethora of dive shops to choose from (over 40 actually).
the island is very small and mostly served by small scooters.
I fully understand and agree with your logic of keeping your bike close by.
It's a nice bike and i'm actually looking for one so let me know if you want to sell it or rent it to me ??
There are slow overnight freight ferried serving the island, I know one goes each night from Chumpon (maybe spelt wrong) which is the mainland port for the ferries serving the islands with the traffic from the North (Bangkok).
don't know the company, don't know the schedule, don't know the price but just turn up at port and expect to get on that nights ferry.
accomodation here can be from about 300baht per night for a hotel 1 room (would sleep two), or there are plenty of opportunities for longer term 'bungalow' rental, prices can be as low as 3 or 4,000 baht per month and up to about 12 to 15,000 baht.
Food - budget about £10 ($20) per day and that should cover everything.
Dive Master course is about 30,000 baht (SSI) you are unlikely (VERY unlikely) to get any income from the school you are with, but you will get as much diving for free as you want AND you can take as long as you want, so intheory you could take 6 months ! (that's a lot of diving).
hope this helps