I ended up with a blind Bedrosian, but managed to salvage the relationship when I talked to her in Sickbay, and confided in her about suspicious goings on later in the game (if you know, you know).
Spoilers for later in the game:
However when I beamed up all the Tkon receptacles, she went off the wall at me, and tended her resignation from the Resolute. When I said I didn’t accept it, Bedrosian said she expected as much and had already filed the paperwork with Starfleet Command. As a result, I only has Westbrook and Urmott to choose from for the new XO. Which resulted in Urmott getting pissed off at me then. Michael Burnham never had these problems when she mutinied…
I just finished my second playthrough. This time I saved Bedrosian instead of the Alydian transport, but it doesn’t really make a difference as to whether she stays or resigns. If you choose to save the Tkon vault she will resign whether you spared her sight or not. I assume that means if you destroy the vault, she will remain whether you rescued her or not.
That bit stuck out to me. I immediately checked the relationship tracker and it says she may never forgive you for this, but very next scene in sickbay she says it’s ok for all the obvious reasons of saving lives, duty, etc.
Then later in the game she throws it back in your face. Couldn’t tell if writers were intentionally doing a flawed character moment or just being inconsistent.