I used to audit bursary applications for several well known London schools and bursaries were, without fail, only given to those children who could bring something to the school either academically, in sports, music or the arts, or they had an exceptional reason e.g. a parent dying midway through their education. Usually the bursary would “top up” a scholarship the child had been given. You are right, OP, that bursaries are not technically granted based on merit (as opposed to scholarships which are), but in essence they are. I have never seen one offered to a child who scraped into a school who couldn’t bring something extra. Otherwise how on earth do you decide who gets one?
Also remember that girls schools, even the very famous old ones, have much smaller endowment pots from which they can allocate funds. Eton and Harrow have large numbers of boys receiving very high fee deductions each year. It’s not the same at Wycombe Abbey.
I absolutely understand that you want your daughter to go to this school. I understand you would do anything to get her in and don’t blame you for trying. But ask yourself, if I was the one making the decisions on money, what would make me choose my daughter over the one who got full marks on the entrance test? Or the one who plays the piano at Grade 7 and cello at Grade 6? Or the girl representing the county in hockey? Every child is unique and brings something to the school community. When it comes to money though, private schools want to invest in those children they can show off about.
Your daughter has a wonderful supportive mother, that is evident. But please do be realistic. It might seem like the end of the world at present but you do have other options. Try taking the 12+ or 13+ for the Grammar - giving yourself a whole year to prepare.
Work on saving like crazy over the next five years to send her to private school for sixth form.
Think about her strengths and work on them over the next two years and try again at the private school for the 13+.
Work on all options but your priority should be preparing your daughter for going to your state secondary in September. You might have a nice surprise but it is looking unlikely.
Coming from me who failed the 11+, went to a Birmingham comp and then onto Cambridge. All down to my hard work and great parental support - the school I went to didn’t define me.