A: To refresh, Captain on the Bridge calls for the Bridge and “one of” Kirk/Picard, and The Bridge of the Enterprise calls for the Bridge and “one of” either version of the Enterprise.
We considered that it might make thematic sense for Captain on the Bridge to have a requirement for a maximum of one Captain, but The Bridge is standing for the bridge of any Enterprise, and, since the Captains are identical in wording, gameplay-wise, it makes more sense for it to be an and-or situation, where you can win with either one or both*, plus the Bridge.
We figured if both captains are on “the bridge,” it’s bound to be the bridge of one of them, and the other is just visiting. It doesn’t matter which one is which, you still definitely have the captain that goes with that bridge, since it’s not specified which bridge.
*If you are bold and lucky enough to combine yet more Star Trek versions using this expansion, any other Trek Captains (Sisko, Janeway, and of course, Archer) would also count as “a Captain.”