My wild Red Valley take is I actually think Bryony liked Gordon. I actually think Gordon is the only person at Red Valley she liked. Up until the moment she got fired because of him of course.
Like obviously she needed him to get information on Aubrey. But she could've interrogated and then got rid of him the moment Warren was in the pod. And she didn't!
She didn't like Clive, she wasn't happy with Pam and Grace and the only reason Warren was involved was her desperation. Her boss, her assistants and even her test subject were all not her choice. But you know who was her choice? Gordon Porlock.
She thinks they're similar and she wants Gordon to see and accept it too. She thinks he is competent which is a lot coming from Bryony. Especially since Gordon himself is not qualified for any of this. He's not qualified to address a scalpel wound, he's not qualified to manage the mental state of The Most Traumatized Person Ever and he's not qualified to look after a facility full of complicated and expensive equipment. And yet she keeps him. Of course, she is condescending and derogatory to him but I think it's just the way she is to people.
I don't think they could've been friends in another universe. And I don't think she cared. But I do think she liked him. Maybe she liked him as one might like an ant. But she liked him nonetheless.