Have you considered applying In Year. My DD just missed out on her Essex 11+ and we put her down for an in year application and she took the entrance exam last week and has just been offered a place to start after half term at our first choice grammar. You could appeal and put her down on school's waiting list for in year admission as well
I may be wrong but I don't think Bucks works this way. I think you 11+ score stands for the whole of year 7 unless you are deemed qualified via review / appeal. For entry into year 8 you would need to qualify via the 12+.
Sally Anne's thread at the top of the page contains loads of useful information. Have a read of that and I'm sure the folk on the Appeals forum will be able to guide you through the process.
The exception being rgs when it has spare seats due to drop outs it does in year admission tests.
The most important thing to ask is what her prediction was, 1:1,,2:1, 1:2 etc and essentially how many with your childs prediction did actually pass, they are reluctant to share this info, but put the pressure on as bcc will know, so why shouldn't you and you would have to know in the event of an appeal. Also clarify her grades/achievements since key stage two and the end of key stage one (hopefully level 3 as seats were used then) and check for any anomalies or glitches and make sure you know why they occured. Check predicted year six achievements are what you anticipated and ask why if not.
Good luck x