The most appropriate mode of transport for you trip will depend on the country you are travelling to and the locations of the gardens you intend to visit - so it is important to plan your transportation before you set off.
Urban bus travel is generally simpler in Continental Europe and Asia than in Britain or America: they have more busses, better timetables and easier ticketing systems.
Coach travel is best organised in Asia, America and Britain. This is partly because of competition and partly because Continental European countries discourage coach operations which would divert revenue from railways: in part-compensation, urban bus companies reach far into the urban hinterland. This is a great help for bus and coach travel to places near towns.
For public transport within London Transport for London.
For bus travel & timetables within Britain see UK Bus Transport Web Directory.
Urban bus travel