Did this trip last Friday with my daughter (7) and thought it might be of some interest to some visitors.
The timetables probably link up better on a Saturday and you aren't limited to travelling after 9am.
Bought Strathclyde daytripper ticket (www.spt.co.uk/tickets/daytripper.aspx) and got the train out from Glsagow Central to Wemyss Bay (lovely station) and walked straight down to pier to connect with the ferry to Rothesay (www.calmac.co.uk). On this calm sunny day the views were fantastic. On arrival in Rothesay it was a short walk to the bikeshed (www.thebikeshed.org.uk) where we hired a child and adult bikes (plus helmets) for a couple of hours. Headed towards Ascog as that was pretty flat and the pavement wide as daughter not confident about cycling on road.
Would liked to have had a game of putting but had made plans to get the bus (www.westcoastmotors.co.uk) to Dunoon which took us across the Colintraive ferry route to the "mainland". Quite a twisty single track road at times so happy to be on the bus and take in views.
On arrival at Dunoon had time get in a quick game of putting on the 9-hole course next to the ferry terminal.
A bonus was that the Waverley paddle steamer was leaving from Dunoon so we got to see that from our ferry on the journey to Gourock. Then train from Gourock back to Glasgow.
I think we could have bought an island hop-scotch ticket that would have been slightly cheaper but I chose to just get single ferry fares as that left the option staying longer in Rothesay and returning to Wemyss Bay. The daytripper ticket is not valid on the Rothesay to Dunoon bus service.