Should I get a playmate for my lone pet mouse?

I had my black-and-white mouse Screwball for a whole year now. It's a girl and I heard female mice are very social. I did have two mice before but unfortunately one of them died two weeks later after I first got it, leaving Screwball all alone for 12 months. :c

Screwball usually just sleeps in a toilet paper roll I place in her tank all the time and only comes out to eat. (Do mice with playmates usually sleep in the day or do they play with eachother?) At night she runs in her wheel for hours. In her 10 gallon tank she has a food bowl where I have her hamster seeds, a water bottle, a hamster-sized running wheel, white pine bedding, and a couple toilet paper rolls. I don't really have any toys for her to play with or a hut for her to sleep in.

Occasionly I'd give her shredded carrots and little pieces of bread which she adores to eat; and play with her. Is that enough to make her happy or does she need a little mouse friend? Would adding just toys be enough to make her more content?