Not quite sure how far in towards Orpington you are but there is a bus that comes through Badgers Mount and then drops down into Riverhead and goes onto the A21 at Chipstead, its the BM1. It's a public bus (but it would be a brave member of the public who got on it
) and they can use the freedom pass. It's very reliable and works well - they look at it as part of the fun, DS1 hated the bus for the first term or so (be prepared for that I think it is quite common) but now it's part of his social life.
There is also the 402 that goes from Bromley to TWells - worth looking at depending on where you are but I think it may take longer as it goes through Sevenoaks and Tonbridge town centres rather than along the A21.
If you google travel to Skinners it will give you all the options. There is also the train option but it is quite a hike at the other end from either TWells or High Brooms stations.
Sorry don't know anything about the private/contract buses as we have always used the public ones. Feel free to pm me if you want more detailed info.