Women would have used rags for towels. I don't know whether they shaved their body hair, but they went in for plucking their eyebrows and hairline (a high forehead was thought to be attractive).
It is not true that medieval people did not bathe, medieval art is full of pictures of people bathing, and some palaces and monasteries had indoor plumbing. The common people would probably not have bathed so often, as filling a tub manually would be a lot of work, but public baths were popular in medieval towns.
It is most unlikely that Queen Elizabeth I would only have bathed once a year. Her palaces had bathrooms with plumbing, and it seems unlikely that she would have used them as infrequently as once a year.
Gervase Markham's book 'The english Housewife' (published in 1617) contains, in the chapter on distillations,a recipe for Rosemary water ofwhich, he says:
'Rosemary water (the face washed therein both morning and night) causeth a fair and clear countenance: also the head washed therewith, and let dry of itself, preserveth the falling of the hair, and causeth more to grow: when one maketh a bath of this decoction, it is called the bath of life: the same drunk comforteth the heart, the brain, and the whole body, and cleanseth away the spots of the face:'
'The Tudor Housewife' by Alison Sim
'The english Housewife' by Gervase Markham
'Down the Plughole: an Irreverent History of the Bath' by Steve Dobell