- You may be looking for the Shadow World version of Moira.
Moira and Bill had a strained relationship, often resulting in arguments or passive aggressive spats. (TV: The Pilot, Extremis) Still, Moria did seem to love Bill and was very defensive of her, despite not fully understanding her. (TV: The Pilot)
Moira had no permanent partner. Neville was her ex-boyfriend and Barry was Moira's friend. (TV: The Pilot) Bill didn't like learning the names, as "I only get attached", and they were all so fleeting. (TV: Extremis) Moira was not aware that Bill was gay, and assumed she was interested in men. (TV: The Pilot, Extremis) Moira had "very strict rules about men", regarding Bill, (TV: Extremis) and told her once, "You need to keep your eye on men." She was very sceptical of Bill being tutored by the Twelfth Doctor.
On Christmas 2016, Moira found pictures of Bill's birth mother in the back of a cupboard. Later, in 2017, when the flat was attacked by a sentient oil creature, Moira was with Neville again in the pub. Bill knew this because Moira called her on Neville's phone. (TV: The Pilot)
Bill moved to her own place for a while, but this soon fell through, as the house was eating her housemates, (TV: Knock Knock) and she soon returned to living with her foster mum in the interim, while in search of a new place to live. (TV: Extremis, The Pyramid at the End of the World)