Our lot get a lunchtime detention the same day if they are one minute late. No exceptions. And if they do it twice, it's a 90 minute detention on Friday. It's improved punctuality hugely in all but a handful of students - and they are largely the ones who are either regularly in trouble for other things throughout the day or they are girls who need to draw on their eyebrows and apply false lashes and contouring before they leave the house
I'd suggest leaving it to her to sort herself all the way to the bus station, letting her sit the detentions and filling in your application to a nearer school, as half an hour late for a GCSE examination means a fail.
But I would, if I were up so early, walk into her room at 6am and draw the curtains. I hate getting up, it doesn't suit me at all (I cannot go to sleep before 1am, ever, never have been able to) - but what does work is light. Electric light hurts, but daylight doesn't. And I'd quite possibly commit murder if somebody dragged my covers off me when I was in deep sleep, which I often am just when I need to be waking up
The other thing is most people sleep in 90 minute bursts, so timing her bedtime so that she is all done and in bed a half hour before one of those times comes round - so, to give her the chance of nine hours (or seven and a half, which isn't enough, but better than six), she needs to be in bed, lights off, no phone/TV a full nine and a half hours before her getting up time. Which, if she is supposed to get up at six, means she needs to be in bed by half eight.
I find that if I'm not asleep at 1am, it's guaranteed that I will be fully awake until either 2.30 or (worse) 4am. I go to bed by 11, just in case my body finally decides to let me sleep at 11.30pm, as at least I am resting, rather than clattering around the house, watching rubbish on TV or twatting about on the internet without a blue light filter. In addition, if there is one light on upstairs, I will instantly snap wide awake - so no brightly lit bathrooms or bedrooms.
It's crap, not fitting in with how the world works. But you have no choice until you're old enough to get a job where your start time is later.