Bowman said the incident happened on the 09:32 GMT departing train from London Paddington, which terminated at Cheltenham.
She said she reported the incident to British Transport Police. The force has been contacted for comment.
“If you are that person who took someone else’s luggage off the train between London and Kemble, please can you return it to the nearest station? I’d really much appreciate that,” she said.
Bowman described the suitcase as dark green with brown straps and appealed for anyone who saw someone get off the GWR train at Didcot Parkway, Reading or Swindon to get in touch with her.
The presenter is best known for hosting BBC Radio 1 shows from 2003 to 2014, when she left to work on other projects.
Bowman currently hosts podcast Soundtracking, in which she interviews guests about music and film.