The Crystal Bucephalus was the result of experiments by Lassiter and Matisse. He dismissed her when he found out she was working with Arrestis. She developed the Exemplar, which could secretly control the time travel equipment at the Bucephalus.
When she learned Arrestis' true identity and plans, she abandoned him and tried to steal the Doctor's TARDIS. She accidentally dematerialised the TARDIS, and it got stuck between the time spillage from the Bucephalus and the Exemplar.
When Garrett led Tegan, Sven Tornqvist and Matisse to the safest part of the TARDIS as it broke up, they went through the library. Matisse could not resist grabbing various books on time travel. This slowed her down, and when the library dissolved, she was flung into the Time Vortex. (PROSE: The Crystal Bucephalus)