I don't own Doctor Who, or Back to the Future which inspired the time-travelling car. I wish I did, though - I could use the cash.
X
Back into Time and Space and the Future.
By TimeTraveller-1900.
The Doctor was excited despite the risk. After he had managed to steal the Master's TARDIS after that business with the Daemon, Azal which had threatened the lives of not only the stupid villagers in Devil's End, a village famed for the connections to the occult and witchcraft, but also the entire human race, which the Daemon, a member of a highly advanced alien culture, and deemed a scientific failure, the Doctor had the entire universe to travel through, and since the Master would never tolerate travelling in a TARDIS with so many faults to the guidance and destination systems, the Doctor knew he would arrive when and where he wished to go.
Finding and using the Master's TARDIS was not difficult. When the Master had first arrived on Earth and the Time Lord - officious bureaucrat though he was - informed him, the Doctor had begun building detectors to help him locate the Master's ship even before materialisation. After their last encounter, the Doctor had collected some of the Master's biodata which had been left on Bessie's steering wheel, and he'd used the Master's biodata to shut down any security system his old friend had installed. The Master knew he had been exiled to Earth, and that he would be desperate to escape his captivity.
While he hadn't anticipated the Doctor making off with his dematerialisation circuit, that business on Uxarieus had made him take precautions to stop him doing anything else. The Doctor had no desire to go through any of them, and so he had shown the Master's TARDIS the biodata of its pilot to let him use the ship himself.
But the Master was wrong.
The Doctor had no intention of making off with another TARDIS despite the temptation. When the Master had first come to Earth and he'd discovered how useless it would be to adapt his own TARDIS to the Master's dematerialisation circuit, the Doctor had come to the conclusion that he would be extremely lucky to get the TARDIS working again. The business with Axos had been a significant step towards regaining his freedom, although he'd still need to do a great deal of work about removing the control the Time Lords still held over his ship.
He had known he could use a different time machine to restore his freedom to move in time and space and while it was spitefully tempting to steal the Master's TARDIS, or even the Monk's TARDIS after the time meddlers' visit to UNIT to get revenge on him for stranding him in 1066 (the Doctor felt more shame for his choices at the time), the Doctor had no intention of letting his rival go through the same thing, not since he had gotten used to the possibilities of getting a different form of time machine.
But where and when should he go?
The Doctor knew he could get a vortex manipulator or two. But they were rather crude and nasty time machines, but he could find himself something else. Running a finger along his jawline thoughtfully, the Doctor considered his options, and thanks to the extensive information in the Master's TARDIS, he found enough choice to decide where he should travel to.
Eventually he decided to head for the 51st century anyway.
Ten minutes after his arrival, the Doctor smirked as he drove a time travelling car towards the TARDIS doors while he was being chased by a few indignant security guards. The Master's TARDIS doorway expanded to allow them inside, like a boa constrictor's mouth widening to accept a much wider and larger animal.
Once he'd stopped, the Doctor jumped out of car, and he dashed to the console and made the preparations for takeoff, setting the controls to land near the road close to Devil's End once he remembered that while the TARDIS could get in and out of the cavern easily, the time car wouldn't be able to fit, even if it could dematerialise itself.
When the time car, the Chrononexus 3000, was out of the Master's TARDIS safely, the Doctor sent the TARDIS back to the cavern. The Master would return for his ship. He knew it. The last thing the Earth needed was the threat of a desperate and dangerous renegade Time Lord who wanted to escape their captivity. The Doctor had been living on Earth in exile with some of his brain wiped of the knowledge needed to help him escape, but he was a long way from being desperate enough to cause pain and mayhem.
The Doctor took the time car back to the cottage he had purchased with his UNIT salary.
X
As far as his UNIT colleagues were concerned, everything was status quo, however there was a sense of delight that permeated the headquarters of the supposedly secret organisation for months to come. With the Master locked up, there was an air of excitement. The Master had been one of the worst enemies UNIT had ever had to deal with. They knew he was a member of the Doctor's race, a time traveller with the same near infinite amount of knowledge and yet he was willing to do whatever it took for power. Many UNIT soldiers had been killed because of the Master's actions in the past, and they were glad to see the back of him.
A prison was being prepared for him after the Doctor had spoken to the authorities on the Master's behalf, although many of the soldiers grumbled about it. Many of them would have been happier to see the Master dead. None of them really understood the Doctor sticking up for the evil Time Lord, and while Jo and the Brigadier and the others who worked more closely with the Doctor than others understood it better, some of them considered whether or not life would be better without the Master around.
For the Doctor, it was business as usual. He would arrive at the laboratory and begin work on the TARDIS, and he would help prevent alien calamities. While he had access to a new time machine, not only would it look incredibly suspicious that he had just given up on getting his beloved ship working properly again, but the Doctor really did enjoy this aspect to his exile; before when he had been travelling in time and space, he had been forced to leave quickly in a hurry to prevent the Time Lords detecting his presence. The Doctor had always been afraid that his interference would lead to the Time Lords finding it easier to track him down, but after a while he had realised it wasn't going to happen unless he happened to interfere in the timeline more than he had thought he had, but by habit he left as quickly as he could. As a result he had come to neglect the TARDIS's systems, and his maintenance of the old girl was rare.
But now he was exiled and in one place the Time Lords knew of, the Doctor had more time on his hands to do some work.
At the same time, while his days were busy whenever he wasn't working on a case or when he decided to put some time in-between the moments, the Doctor was free to travel in the Chrononexus-3000.
X
Once he had the time machine, the Doctor had needed to not only learn how to use it but he also had to work out how he was going to use the Chrononexus 3000. Fortunately there was a manual that he had no trouble going through; it wasn't as complex as a TARDIS manual. There was no micro universe for him to maintain, no circuits like a perception filter or a chameleon circuit. But he quickly mastered the basics.
The Doctor eventually decided to take the Chrononexus 3000 on small trips, rather than just simply leaving UNIT behind in the lurch although it was tempting to do it, especially when the Master escaped again. But when he did leave, he made sure to do it without anybody knowing and he always made certain that he came back in a few months for him, relatively speaking.
When the Time Lords eventually gave him back his freedom as a reward for stopping Omega, the Doctor's memories of time travel returned and he was able to remove those accursed protocols keeping him from leaving after the Master restored the dematerialisation circuit following the mess with Axos, he realised he didn't want to throw the Chrononexus 3000 away.
After all, why have one time machine when you can have two?