But after traveling for less than a mile, she was targeted by Moran, who dragged her into a park and launched a "savage" attack which was "almost devoid of any mercy".
The 19-year-old, who was high on drink and drugs, then panicked when he spotted a passing police patrol, approaching it and claiming he had come across the injured, semi-naked woman while walking through the park.
It was a lie Moran, who denied rape, persisted with throughout his trial. But he was found guilty of the charge, and one of wounding with intent, by a jury following four hours of deliberations.
Moran, of Nottingham, was handed an indeterminate sentence for the protection of the public, and told he must serve a minimum of six-and-a-half years in before he is considered for release. Even then he will only be freed once he is no longer regarded as a danger.
Judge James Sampson said Moran, who will begin his sentence in a young offenders' institution, had carried out a "brutal and horrific" attack upon his victim, and had not shown "an ounce of remorse or shame" for what he had done.
He added: "She was a 23-year-old student, intelligent, hard-working, brave, full of the optimism of youth, and delightful, who for the want of a small act of kindness was left isolated and vulnerable in this city in the small hours.
"Using extreme violence, you stripped her naked and battered her so violently her own mother did not recognise her. This was a sustained attack lasting some 25 minutes."
Michael Auty, prosecuting, told the hearing the attack was "every parent's darkest fear and worst nightmare."
He added: "The effects have been this: From her perspective and that of her wider family the smile that they all knew for so long has gone.
"She bears physical scars. Every time she smiles, every time she eats, every time she tries to do something as simple as applying lipstick or it is cold, she is reminded of the events of that day. Her confidence, if not shattered, has been severely dented."
However, the court heard the courageous student had returned to her course following the incident and had achieved a good grade in her law degree. She is now planning to begin a legal career.
The attack took place in December last year.
Moran's victim had been out celebrating the end of her graduate diploma in law exams when she boarded the last bus home in Nottingham city centre.
Mr Auty told jurors during Moran's trial: "The fare was £5. She had only £4.80. The bus driver would not waive the 20p.
"She asked him if he could wait while she got some money from a nearby cash machine. He refused that request too.
"She was effectively turfed off the bus and left stranded in Nottingham city centre at 3am in the morning."
The court heard the victim started walking to meet her mother - but was grabbed by the neck and dragged in to Nottingham's Forest Recreation Ground where she was beaten and raped.
Her "substantial" injuries included black eyes, a badly swollen face and bruises to her body, breasts and neck.
Mr Auty told the jury that "in the cruellest of circumstances" her mother had pulled up on a stretch of the road where she expected her daughter to be walking, and just yards from where she had been attacked.
She called her daughter's mobile phone twice and on both occasions could hear a "grunting" before the line went dead.
Police in a passing patrol car then stopped to ask if she was all right, and she explained she was looking for her daughter.
Then, within moments, Moran appeared, ran to the police car and banged on the roof. He told the officers: "You had better come quick. I think a girl has been raped or something".
He claimed mud and the victim's blood were transferred to his body and clothes when he tried to help her to her feet.
Moran's victim was found nearby sat with her knees pulled tight to her chin. She was naked from the waist down, and her injuries were so severe that her mother didn't recognise her at first.
Mr Auty said Moran, who was two-and-a-half times over the legal drink-drive limit and had traces of cannabis and cocaine inside his body, had "panicked" when he spotted the police car and tried to make out her was "her saviour, her knight in shining armour."
In a video interview the student recorded with police officers after her ordeal, she described her experience on board the bus, saying: "I remember having a gross sense of injustice that he (the driver) wouldn't let me on."
She also revealed that she found it "really depressing" that she had not been allowed to travel on the bus.
The victim said her last memory of the night was walking towards home alone. She could recall nothing about the attack and her next memory was waking up in hospital about 8.30am the same day.
After Moran's conviction the bus company that employed the driver who turned the student away admitted he had ignored company policy and had been disciplined.
Alex Hornby, commercial director at Trent Barton, said: "Our drivers are well known for looking after people and there have been many examples of exceptional service by our teams, even including paying their own customers fares out of their own pocket.
"Sadly on this occasion this did not happen and our driver did not follow his training.
"The matter was dealt with through our disciplinary procedure within days of the incident last December."
When asked about the outcome of the disciplinary process, a company spokesman said: "A disciplinary matter is confidential and remains between the employer and employee."
It is not known if the driver is still employed by Trent Barton.
Detective Chief Inspector Rob Griffin, of Notts Police, said: "The level of violence was so extreme it was shocking.
"Nottingham will be a safer place by virtue of the fact Moran is in prison, and the females of the city are much safer for it.
"He is very dangerous and very violent. He is a sexual predator.
"It is tempting to start to attribute blame, and one might try to blame the driver of the bus. But had she got on the bus, I think he would have attacked someone else. The only person to blame is Joseph Moran.
"It is difficult to speak for the other passengers on the bus and they made a judgement that night. Knowing what they know now, they may have given her that 20 pence."
