ariane5, good luck, and try not to beat yourself up. As others have said, you have to go for the long shots otherwise you never know. If it had worked out, you would have done the right thing - and it might have done. If they say she is on the bursary waiting list then you can't have been far off - if the (I suspect very few) people above her had not applied, or passed the exam.
I am no expert but I would now do two things I think: get some specialist advice on what sort of provision the allocated school can and should make, and contact them as soon as possible to get the ball rolling (maybe post on the SEN board for advice about any organisations that could help you); and talk to the bursar or registrar of the independent for your own peace of mind, and so that you know the situation if you decide to have another go - it is also worth asking f they have any advice (you never know).
Even on a small site, there can be a lot of walking around depending on how the timetabling is done, and how the routine of school life pans out for a particular individual (if they happen to choose clubs at opposite ends of the site for example!). And schools seem to vary massively in how they organise the timetable - some keep yr 7/8 in one classroom or small block of them, and teachers come to them.
As your dd's problems will be apparent (presumably to her classmates), I think I would also approach the school about this, ask how they manage it, what information the other kids will be given, how they deal with name-calling, the detail of the bullying policy, and so on.
You sound like a wonderful mother. Good luck to you all.