Moving up to high school, do they take themselves to school and back ?

Start with little steps at a time: when you are walking to & from primary school let her walk in front of you; then let her set off a few minutes before you. You'll want her to get used to her front door keys so make sure she gets home before you. And on the buses let her sit some rows in front of you and decide when to get off.

As a secondary school kid she'll be mortified if you were to tag along with her. You've got about 9 weeks of term and 6 weeks of holiday to practice. She'll be fine and love the independence.

Yes, she should be getting herself too and from school if it's only a bus ride away.

You'll need to do the journey a few times with her so she knows the ropes, and make sure she has a mobile phone that's charged up and in credit in case of emergencies. Find out if any of her friends who live nearby will be making the same journey. DS used to meet up with a couple of mates at the tube station and they all travelled together.

Part of your problem is, the bit where you say she has never gone anywhere by herself.
You mean she's already 11, and never gone round to a friends, or to the library, or the park, or to post a letter, or go to the local shop ?????
I think you need to start letting her practice all these things NOW. she needs to be able to judge traffic, etc.
The actual bus journey, you'll find quite a lot of parents going on with them in the holidays, to show them the route and where to get off, and then on again to come home.
Why not let her walk to and from school now, on her own (you can set out a few minutes later with her sister), to at least get used to that journey which she already knows well.

My DS is in year 6 and I have exactly the same issue as you. I currently take him and his sister in the car, but will not be able to in September. Over the last month, I have started letting him get the bus home by himself three days a week. He was nervous at first but now thinks it is fantastic. I then got him a childrens oyster card and he is so proud to be using it and feeling like a big boy. Last week I let him take his mobile phone to school for the first time, just so he learns about only taking it out when he needs to and not advertising it to older kids, this was fine as useful because I could call him when he was 0.00001 second late home!! Yesterday I let him collect his sister and bring her home on the bus (she is Year 4) and whilst I felt sick with anxiety, they though it was brilliant.

I am no longer worried. He will be fine and I have cover if I need my DD to be collected. I hope it does not change when he travels with his friends in September and wants to 'hang out' rather than coming straight home.

Yes! At secondary they don't want to be seen dead with parents!

I 'trained' my two (who both walk to school though bus is option) by walking with them so they knew the route, then behind them at a distance. Also let them do errands on their own to build up confidence. So you could do the same thing but by bus - so she knows how to buy a ticket, how to get off and exactly where etc.

By the end of her first fortnight it will be as though she's never done anything else

Is it a dedicated School Bus? My DD started getting the bus to school towards the end of Y5, but it is a school bus, they were seen across the road after school, and the bus stops right outside our house .

Are there other pupils doing the same journey from the same stop? I think it is the norm, so definitely get her used to the travails of journey by bus.