There are pupils I teach who didn't attend for long periods purely because they hate school. The environment, the people, the smell... anything. They just can't bear being there. I think sometimes people underestimate how 'traumatic' it can be for some pupils when the move from primary to secondary. I remember being terrified of the sheer scale of the building when making the same transition. It's not always bullying.
I'm sure you've already done this, but I'd suggest the following:
1) Speak to her head of year/pastoral leader/tutor or EWO. See what they suggest. Perhaps they can speak to her at home to try and get her to school for a meeting.
2) Explain to her, as if she's an adult, the consequences of her actions. The fines, the cost to her education (95% is just satisfactory) and her being taken into care.
3) Part-time timetable? Purely to get her re-integrated.
It's a very difficult situation for you to be in, so I appreciate that. Was she a well-behaved, high attaining pupil prior to secondary school?
If it makes a difference, she sounds like a girl who has just recently started attending regularly. It got so bad for her that her hair began to fall out - around Year 8. She's now Year 10, still very quiet and withdrawn, but is becoming a successful student.
Good luck.