What YummyHoney said is good.
You need to pinpoint the things that only that school can provide for your dd, and why she particularly needs those things.
I don't think the fact that it's closer will have much effect as she is already doing a lot of travelling on her own, so you need to be able to say why that is detrimantal to her, and why the shorter travelling time will benefit her. Has she suffered any bullying on the journey or anything like that? You do need to say more than just 'it's safer'.
As for her having friends there, that's not a bad reason, but again, you need to be able to say why the support of her friends is particularly important to her. What effect will it have on her if she isn't with them? How does her shyness affect her?
Have a look through the school's OFSTED report and their prospectus to see what they offer that would make a difference to your child, specialisms, or GCSE options (as has already been said) pastoral care, anything at all, and give reasons why your dd needs those things.
Don't be afraid to use any little reason you can think of, and don't assume that the panel will think something is irrelevant. Say everything and let them be the judges. You also need to provide evidence for the points you are making, so for example, if you say that your dd is excellent at languages and the school has a language specialism, provide school reports or anything else you have that proves she really is good at languages.
Hope that helps. Good Luck.