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." (TV: The Pilot)
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) Moira doesn't know that Bill is gay. The Pilot (TV story), Extremis (TV story).