At the time Savile was in his performing prime he seen by most of the public as just an eccentric odd ball. Travelling regularly between London and Leeds c79-83 I used to see him on the train occasionally. People greeted him as the Celebrity he seemed to be and for the most part he acted 'in character'.
He was allowed into schools, hospitals and the Prime Minister's country retreat as an honoured guest. The one near miss with prosecution during his lifetime was a result of groping teenage girls in a Children's Home/Approved School. The evidence was, by then, 30 years old and, even if the women concerned had been persuaded, against their apparent instincts at the time, to go into the witness box they'd very likely have been torn apart - metaphorically of course.
The CPS report on why it was not pursued is a window back into the times and, frankly, the opposite of a cover up - too much hindsight and application of 21st Century standards.
Only after his death did it come out that he was a sexual predator and that some people in authority had at least an inkling of what he was up to. The morals of older men interacting with youngsters was completely different in the sixties and seventies. The word Safeguarding and all that now rightly and routinely goes with it had not been invented.
I appreciate that the OP now feels, quite rightly and knowing what we do now, that she was abused but I think dealing with via talking and therapy is the way forward.
Anybody who was teaching then is probably going to be long retired and, with the same hindsight as the rest of society