Bridges, who won the men’s points race at the British universities and colleges championships in Glasgow in February, began hormone therapy last year.
British Cycling’s regulations, updated in January this year, require riders to demonstrate low testosterone levels for a 12-month period prior to competition.
The initial decision to allow Bridges to race caused major controversy, with threats of a boycott from other female riders if she was allowed to compete.
Critics say trans athletes have an unfair advantage even when testosterone levels have been lowered due to the impact of male puberty on the body.
“It would not have been fair to ask Laura Kenny and the other women cyclists that Bridges would have come up against to have to race a rival with the advantages of a biological man,” said former Olympic swimmer Sharron Davies.
By Garrin Lambley © Agence France-Presse