A large number of both Tiffin girls and boys walk from Kingston station, some use train from Sunbury area. Others use train either to Richmond (then 65 bus) or change at Twickenham for Kingston. I think you need to buy season ticket for trains, bus can get free travel on the buses.
The buses are very slow in the morning, traffic between Sunbury Cross and Hampton Court can be very slow and can seriously delay buses. Might be ok for return journey as that isn't peak hours. May be faster with 2 buses (changing to another to avoid worst traffic), try looking at picking up a 285 in Feltham or Hanworth, or a 111. There is also the express X26 (but that is only every 30 minutes)
There is a way of checking the actual journey time of a bus, rather than timetabled time, use www.lvf.io
enter the route number, note a bus registration or fleet number nearest your stop, then look again in 15, 30, 45, 60 minutes etc and see how far it has got. Start looking at 7am based on aiming to arrive at school about 8:15am