Regardless many men or not the story shows within her circle of contacts she had several men of interest - and maybe a few more among the 'Boys' who played darts but more, she was 31 and in the 1950s a women 31 years old was not what a women today is like at age 31 -
They were more settled, they dressed as mature women, there was not a menu of jobs for women and those who had jobs were relegated to secretarial, department store sales, not yet even teller's in a bank, teachers, nurses and airline stewardesses. And so, women living on their own were counting pennies.
A women alone was limited in after hours activities - there were still separate entries to many bars and restaurants with bars in the US - I do not know about the UK - but except for a movie, museum, library, cafeteria there were not too many places for a women to spend her after-hours except at church centered activities and at home. You do not meet scintillating men at home or in any of the public places approved for 'nice' women much less
'excellent women'.
My thought is Mildred became who she is because of her childhood - her mother died while she was still in school - she has no one during those teen years to help her build her self-confidence - to help her sort out who she was – help her come to terms with her pain. There was no family member mentioned or even a teacher who acted as a mother figure that she could talk to if she was working through her mother's death – an adult who was there for her to help her with her guilt over feeling anger, which we know is part of grief and for any guilt she may have over something she may have thought contributed to her mother's death - she had a friend and they were both fat - they were not among the accepted group of girls, a way of safely isolating when you feel you are different.
The story has Mildred taking care of her father - He may have expected his life to go on so he did not have to deal with the pain of loss – after all he had the important work of a church leader and his daughter was going to make him feel better rather than he, as her father, the adult, taking it upon himself to make her feel better. She finds fault with men and yet, feels she needs to take care of them - sounds like she is still working on what she needed and didn't get from her father.
She did not have a mother who guided her or at least helped her make simple choices so that at age 31 choosing a lipstick and sticking with her choice without knowing how to judge if it was a good color for her is something a teenage girl goes through.
Teen years are difficult - you do not want to be singled out as different and Mildred was different - easy for the girls to say Ahhh and pat her on her head - I do not think she consciously made the choice but she knew she did not want to be the class pet project and she was different so she found one friend and they isolated themselves with schooltime giggles and eating.
Mildred had no one around to teach her parenting skills. I think most women know with marriage most often there are children - this could be something Mildred feared knowing she did not have a clue how to care for a child but then that is me injecting into the story another element that is not mentioned - but what is mentioned by its absence is there are no children in this story - none of the adults care of children.
I see Mildred as someone emotionally frozen in time and is thawing out again without any more guidance than she had when she was a teen. I think her attachment to Dora is greater than that of a friend. She was there when she was isolated from family after her mother died. There is no talk of a Grandmother or Aunt taking her by the hand and helping her through what we know had to be anger, a feeling if she can trust life or others to be there. Some place in her head or heart she must have asked if those who she lets down her guard and loves would be leaving her and dying therefore, she would go through feeling alone and isolated all over again.
It is safer to be alone and not even have a room-mate. A visiting guest is on Mildred's terms by not being there disrupting her carefully laid out life for too long a time - by carefully laying out her life she can control how she feels and avoid unresolved issues after the death of her mother and father.
I feel this has to matter or why would Barbara Pym bring the parents and their deaths into the story - others in life may have been able to get beyond a similar life experience and yes, many women did take care of a widowed father without becoming a spinster just like some folks live through hurricanes, floods, wars and other disasters while some or injured and some do not make it. Mildred appears to me to be one of the walking wounded.