Yes Cheam Station is the closest to Nonsuch and it's only a 10 minute walk. It's very safe, lots of shops and other pedestrians and safe crossing to the school (and the odd coffee shop which the girls make use of too
). From that direction, the girls all use the entrance in Nonsuch Park, but it's very busy in the morning and not a safety problem at all.
I'm not aware of a bus that drives into the school. The 470 goes past the front gate and there used to be the 808 which was the dedicated Nonsuch bus from Stoneleigh, but that was cancelled 2 or 3 years ago now.
Do you want to say roughly where your DD would be travelling from? Obviously getting the bus would be cheaper but the train avoids the traffic that can build up around Cheam.