Pathways in Time
Story 2 – Doctor Jones, not Indiana
How the Doctor met Martha, or at least how I wish it would happen.
He spends a few years, not days, aimlessly adrift; putting his mind to other tasks, such as configuring a new Zero Room to the TARDIS, and doing repairs below the floor. He does a few test runs of systems, throws himself into a few wars on distant planets.
He doesn't go near the Sol system, or the little blue planet. Not for a long time.
Then a glitch in the space-time coordinates throws him into the not-so-far future and a little off-course from his original destination of Lerkos Hal, landing him smack in the middle of the gardens at the University of Mars under the Galactic Republic of Earth.
He reflects that it is somewhat silly that they call themselves the Galactic Republic, when they've barely touched the borders of their little tendril of the Milky Way.
He's not laughing when he finds out the archeology students have woken up one of the forgotten tombs of the Ice Warriors, and they're bent on wiping the stupid apes off the face of their planet.
He finds an unlikely ally in the bright but brash young Martha Jones, MD-in-progress, and only once makes the obligatory reference to Earth media, earning a withering look from Doctor "call me Indiana again and I'll leave you strapped to this Wa'rios operating table" Jones.
He later agrees it isn't as amusing when Martha accidentally trips a hidden booby-trap, and they're running for their lives with a spherical robotic defense drone tearing after them like a bloody great boulder.
When the Warriors are finally sent back into stasis, and he seals up their tomb (for good, he hopes) he doesn't need to ask her twice to come with him. He doesn't even have to ask once.
He found her in the cloisters two hours after dematerialization.