Before you say that it is hard to get to this part of London, think again. There is a railway station right beside Barnes Bridge and another one, Barnes Station where you will exit from the handsome Victorian Station House into beautiful Barnes Common and from which you can take the delightful rural walk into the village. And what's more you can reach it in only 23 minutes from London Waterloo. There are 7 trains per hour. The station is in Zone 3, so if you travel after 9.30am a Zones 1 - 4 One Day Travelcard is the best value way to travel.
Even better, why not take a Tube to Hammersmith. From there frequent buses 209, 284 or 419 will take you to Barnes Bridge in 10 - 20 minutes. The bus station is outside on ground level right next to the Picadilly and District Line Station and across the Road from the Hammersmith and City Line stop. Buses run every 3 minutes, and the buses depart from either stop J, K or S. It's that simple.