The Isle of Bute is by far the easiest of the West Coast islands to reach. It is only 40minutes by car from Glasgow, and around 80minutes drive from Edinburgh. 
Click here for a detailed map of the region from Multimap.

By Air: Prestwick and Glasgow airports.

By Car: roll on, roll off ferries at both Wemyss Bay and Rhubodach.

By Train: from Glasgow Central direct to the ferry terminal at Wemyss Bay.

Useful Travel Links: 
Find a Flight to Glasgow
EasyJet (Flights to Glasgow International Airport)
Flybe
Ryanair (Flights to Glasgow Prestwick Airport)
Caledonian Macbrayne (Ferries to Rothesay)
Western Ferries (From Gourock to Dunoon) 
The Trainline
EasyRentaCar
Car Hire (Prestwick)
CityLink Buses
Once you have arrived on Bute you will find Ivybank very handy for the centre of Rothesay and only a 5 minute walk from the ferry terminal.