Bridget was AMAB and was raised with a twin brother in their village. The village had a superstition where they believed that twins were cursed, and as a result one of the twins would be expelled from the village or sacrificed. In order to avoid this, Bridget’s parents dressed them up as a girl so that she wouldn’t suffer the same fate as the other twins. Bridget later grows up to become a bounty hunter in order to prove that the villages superstition about twins being cursed is a load of bull.
Now while the other 2 games they were in had them as male, the newest game has Bridget come out as being transgender (and the creator of the Guilty Gear franchise even making a statement confirming that Bridget is indeed a trans female).
Noe while the majority of people are happy about Bridget being trans (especially actual trans folk), a few people feel like since Bridget was basically forced to pretend to be a girl for the majority of their life, then then coming out as trans has a lot of unfortunate implications.