Melanie Bush

Melanie Bush, BSc (Hons), or simply Mel, was a computer programmer from the 20th century and a companion of the Sixth and Seventh Doctors. Not unlike River Song, she had a temporally complex relationship with the Doctor, in which she met the Doctor at a different time than he met her. Eventually, however, their timelines did synchronize, and she was able to have a more-or-less linear relationship to the Doctor, starting in the later days of the Sixth Doctor's life. Her temporal relationship to the Seventh Doctor was thus always completely linear.

Personality
Mel was a computer programmer from the 20th century who came from the village of Pease Pottage in West Sussex, England. She had an eidetic memory, and a cheery, almost perky personality. She greeted most situations with a warm smile and good humour, and was an optimist whose views extended to believing the best of people's natures, but could also scream freely. She was a health enthusiast and a vegetarian, often encouraging the slightly portly Sixth Doctor to exercise more.

Her enthusiasm for healthy living was borne of the hard-nosed logic of basic science, which also manifest itself in other ways. She was, for instance, flatly dismissive of the supernatural — like ghosts — as scientifically ludicrous. (BFA: Catch-1782) Equally, she did not believe in the concept of fate. (BFA: The Juggernauts)

She was present (albeit unconscious at the time) when the Sixth Doctor regenerated into his seventh incarnation, and continued to travel with him.

Before the Doctor
Melanie had a keen interest in science from a very young age. Her uncle, Dr. John Hallam — most likely her mother's brother — was deeply influential to this childhood obsession, and she credited him with her later academic success. In 2003, Hallam told his colleague, Professor David Munro, that Mel was "very gifted" with computers. (BFA: Catch-1782) As a consequence of her education, she was adept in the Human computer languages of BASIC, COBOL and FORTRAN. (BFA: The Juggernauts)

Meeting the Doctor, for the first time
Mel first met the Doctor in Brighton in 1989. However, as a consequence of the Doctor's trial at the hands of the Valeyard, he already knew her. Therefore, for a time of indeterminate length, he had to pretend that he had originally met her in Brighton, as well. (PDA: Business Unusual) It was only after she was returned to his future self's side following the trial that their timelines synched, and he was able to progress with her in a more forthright way.

Meeting the Doctor during his trial
Mel first appeared when she and the Sixth Doctor had been travelling together for some time. The events of which were shown as part of a Matrix projection of future events being shown to the Sixth Doctor, so from his point of view, he was seeing an adventure he would have with Mel even before he met her in his own timeline. (DW: The Trial of a Time Lord)

Following the trial
Following his trial the Doctor returned Mel to her original timeline with his future self during an adventure on the planet Oxyveguramosa. (MA: Time of Your Life)

She decided to stay on Iceworld with the galactic confidence trickster, Sabalom Glitz, leaving the Seventh Doctor to travel on with his new companion, Ace. (DW: Dragonfire)

Encounter with the Seventh Doctor following her departure
Encountering the Seventh Doctor he revealed to her that he manipulated her to depart his company on Iceworld because he knew what was coming (as Time's Champion) and couldn't have her as a companion. (NA: Head Games)

Following this encounter she returned to Pease Pottage. (PDA: Business Unusual)

At some point in the future Mel may have ended up on the planet Heritage and died there in the 61st century. However during this point in the Doctor's adventures many enemies were attempting to eliminate his companions from the timeline, thus she may not have died here. (PDA: Heritage)

Alternate timelines
Mel also encountered the Valeyard in an alternate version of the timeline, here she was much more cynical and hard than she had been originally. (DWU: He Jests at Scars...)

Behind the scenes

 * Mel's last name is never uttered during any televised appearance, and the closing credits identify her only by her first name. It is, however, regularly used in Big Finish audios and various stories told in other media.
 * According to his book The Companions, John Nathan Turner planned to begin Season 24 with a storyline explaining how the Sixth Doctor met Mel. This story was never produced due to Colin Baker's removal from the role.