In reply to Luke14:
It's ~£4 return to the top car park from Aviemore - https://www.stagecoachbus.com/routes/north-scotland/31/cairngorm-car-park-a...
As Alex suggests, it's a bit limited, particularly when due to it being used as the school bus there's a 2 hour gap first thing in the morning and the same in the afternoon. Last bus down at ~1700 can be pretty busy if the snow is good.
Having lived in Aviemore and Braemar a while ago I'm similarly not aware of any other public transport to get in to the hills. Depends what you have in mind.