If you seriously think Bridget is trans you have a severe problem or simply wishful thinking that everyone is like you, please learn properly his story and why Strive ruined his entire motivation and character arc.
You guys have to understand once and for all that many times people wish to be the other gender because they see positives that they don't have, it doesn't mean that they FEEL as if they ARE that gender.
How many teenager girls say that they wish they were a boy once they start menstruating? Does this mean they are trans? No they are not. How many men nowadays say that they wish they were a girl because it's easier for women to start dating? Does this mean they are trans? No they are not, regardless of them being right on that thinking.
This character wants to be a girl because from his point of view and the escapism that he found (yuri), women in their game are exactly the opposite of what he is VIEWED by society. Everyone is scared of HIM and wishes he could be soft looking and be able to say cheesy lines without others being scared, so the first thing that comes to mind for him, is his yuri games. This doesn't mean he's trans, he simply has a dream where society doesn't run from him and talks to him. Him being afraid of not fully turning on the first chapter is because of his fear of being found out and kicked from his paradise, he's not afraid of having male genitalia.