It's awkward writing trying to do some sort of justice to a character they introduced 20 years ago with little forethought. To quote wikipedia:

Bridget was created by Guilty Gear Daisuke Ishiwatari, wanting to create a "cute character," initially presenting her as a crossdressing boy, a detail that was kept secret to most staff members.[4][5] Ishiwatari "wanted something unconventional" to differentiate Bridget from other fighting games' cute characters; he and staff members decided it "would be interesting to make the character a guy."[5][6]

Following speculation about Bridget's gender following her addition to Guilty Gear Strive, Ishiwatari and Strive director Akira Katano confirmed that Bridget self-identifies as a woman and uses "she/her" pronouns.