The woman, who cannot be named, told a jury she was in a "panic" when Mr Travis allegedly grabbed her breasts as she went live on air to introduce the programme in the early 1980s.
She told jurors at Southwark Crown Court, London, she did not tell her bosses about the alleged incident "due to the climate at the time" and because Mr Travis was "a big star" at Radio 1.
Another alleged victim said managers at a radio station that Mr Travis later worked at "were 100% aware" of complaints about him from female staff.
Giving evidence behind a curtain, the former Radio 4 announcer - the trial's first witness - said she was assaulted by Mr Travis after he walked into the studio she was in as she was about to go on air.
The woman, who was in her 20s at the time, said the DJ sat down behind her as she read out the time, when she felt him standing behind her.
"His hands came round under my arm pits and he put one hand on each breast," she said. "He started to move my breasts up and down."
The woman told the court Mr Travis held her breasts throughout her announcement, which lasted about 10 seconds.
The alleged victim said Travis sat down after the incident "as if nothing had happened".
Mr Travis, of Buckinghamshire, whose real name is David Patrick Griffin, denies 13 counts of indecent assault between 1976 and 2003, and one count of sexual assault in 2008.
He also denies assaulting 11 women, one of whom was 15 at the time of the alleged crime.
The trial continues.