This argument is senseless: You're arguing about Guilty Gear in a FFXIV forum. But screw it, we're here; when in Rome.
The concepts being discussed on Bridget are likely being made in innocent ignorance: that, or blatant intellectual dishonesty.
At Base
I take them as being a cross dresser (if by force). Bridget was not born into a gender not their own and forced to conform, they were born into their proper gender (one he enforces in conversation in some instances) and forced to conform to the adverse. Bridget is not trans, as Bridget does not need to transition into anything. They are certainly misgendered often.
The Complication
Some of the endings of Guilty Gear show Bridget being turned female as I recall, and adopting this as the primary gender. Others show Bridget fighting to maintain being male, 'refusing to change for the world.' How you want to take these details is down to personal opinion. The dev's are not native speakers and don't understand the nuance in the trans terminology, so I don't particularly trust their take on 'Bridget is Trans' unless you also commit to that meaning 'Bridget is trans in the way that japanese people use the word Trans.' Culture dictates. In the game, the 'good ending' is Bridget telling the world to bugger off and staying male, and the 'bad ending' is Bridget going female: I don't take this as the Dev's saying women are evil, I take this as a testament that (at the time) Bridget was understood to be male and was being pushed into an identity not their own.
The Issue
Either way there is argument that this means Bridget is convinced to be a gender not their own through gender-affirmation. Something that, last I checked, the LGBT wasn't crazy about. Convincing someone to be another gender doesn't make them trans, it makes them a victim of outright evil behavior.
So I'll put it this way:
I don't think the majority of the trans community is going to be sunshine and rainbows if you call something trans in the Japanese context. Which is to say highly fetishized, poorly defined, and incredibly objectifying. I'd like to think Sena was not aware of the massive implications of holding Bridget on high as a standard of Trans characterization and said this in innocent ignorance.
But hey, if the Trans community wants to jump on calling Bridget 'Trans', let them do them, I guess. Seems gross to me but it's not my barbeque.