Want to cycle the Great Ocean Road? Melbourne to Warrnambool, half-way across the state, is $36. To get to the other side of the state, Bairnsdale, is the same price. Halve that if you've got a concession card. To get from the city centre to Lilydale, the start of the fabulous Lilydale-Warburton Rail Trail, is $4.10. Again, halve it for concession.
No need to book
All of the metro network, and some of the regional network use the myki ticketing system. Once you've got your card, and have loaded money on it, simply scan it as you get on and off the train.
The more far-flung parts of the regional network operate on paper ticketing, but that still doesn't mean you need to book ahead. Tickets can be purchased at the station, or on the train itself if you get on at a small station where there's no ticket booth. Click here for more info about ticketing.
However you can book ahead on long distance V-line services if you wish to reserve a seat. This is a nice thing to do as the reserved seating carriages are quieter and less smelly than the unreserved ones. Really, they are less smelly.
Wheel your bike on at no extra charge
The regional train operator V-line's official policy states that they will accept your bike on board if there is room. That uncertainty sounds a bit off putting, but in my experience, there is always room. In the roughly 10 years that I have travelled with my bike on V-line, they have never refused it. However I have never travelled with a large group of cyclists. If you plan to do so, I suggest you contact V-line ahead of time and ask if special arrangements need to be made.
As for the Metro network, the only thing you need to know is: avoid peak hour. At 8am on a city-bound train, there's barely enough room for you, let alone a bike with panniers hanging off it (cue smug laughter of folding bike owners). Same goes with trains leaving the city at knock-off time. Also be aware of events like big football matches, as these can also make trains very crowded. At any other time there will be room for you bike.
And a few things about buses
Officially V-line will not carry bikes on buses unless they're in a box. If it's not boxed, you can always ask the driver nicely, and some of them will take it, but don't count on it. However if your train has been unexpectedly cancelled and replaced by buses, V-line staff will usually find room for your unboxed bike in the luggage area underneath the bus.
If it's a scheduled bus replacement (ie, the train isn't running due to planned track works, etc), it's less likely that they'll take your bike unboxed. Check the V-line website for service changes before your trip. If metro trains are replaced by buses due to track works, you will not get your bike on the replacement bus. Check the Metro website for planned works.
If you're planning a trip on the Murray to Mountains Rail Trail, Northeast Coachlines offer bike transfers in that area. There may be other regional operators that do something similar. Just do some research.