The woman, who cannot be named, told a jury she was in a “panic” when 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 she did not tell her bosses about the alleged incident “due to the climate at the time” and because Travis was “a big star” at Radio 1.
Another alleged victim said managers at a radio station which Travis later worked at “were 100% aware” of complaints about him from female staff.
Giving evidence behind a curtain, the first witness, the former BBC Radio 4 announcer, said she was assaulted by 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 veteran 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 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”.
She said due to “the climate at the time”, she believed she would be told “to live with it” had she reported the incident to management.
During cross-examination, Stephen Vullo, defending Travis, said his client denied any knowledge of the incident.
Travis, whose real name is David Patrick Griffin, is charged with 13 counts of indecent assault dating back to between 1976 and 2003, and one count of sexual assault in 2008.
The 68-year-old, from Buckinghamshire, is accused of assaulting 11 women, one of whom was 15 at the time of the alleged crime. He denies all the charges.
A second alleged victim, who worked with Travis in the premises of Chiltern Radio at the turn of the millennium, told the court that women “kept their heads down” whenever Travis entered their office.
The woman, who was in her 20s at the time, recalled three specific incidents where Travis is alleged to have abused her.
The woman said she repeatedly questioned why she did not complain to Travis when he allegedly touched her breast while reaching for a pen in a second incident. But she finally “snapped” after Travis allegedly approached and assaulted her while she was perched on a desk.
The witness said: “He had both hands on my thighs and began rubbing my thighs.
“He pushed the skirt up. I could feel his fingers against my knicker elastic — at which point he tried to get his fingers under.
“At that point I absolutely snapped. I couldn’t take it any more.”
The trial continues.