They wear sleeveless chemises, very indecent looking.
from the Epistles of Paul (ÖNB 2789, fol. 1r), c. 1395-1400
I concluded that this was specialized apparel, suitable for women of questionable repute who were actively working as bath attendants for men. (They wouldn't have been caught dead outside the bath-house with this getup on.) Chemises that go under your clothes are long sleeved, as can be determined from art and logic- if you want to protect your clothes from sweat, you should have sleeves to cover your armpits. (As Mistress Astrida points out, not all styles of underwear have had this feature - I've seen Victorian dresses with perspiration stains in the armpits - but the 14th century seems to have embraced long-sleeved undergarments for ladies.)
Today I found a reference to the expenses of Queen Joan of Navarre in 1419-20, in which 12 ells (ells measuring about a yard, the length varies) of linen were purchased to make her "stewyng smokkes." C. M. Woolgar, in The Senses in Late Medieval England (p 243), glosses this as "the clothes she wore in the bath." Stewing was bathing, the stews were baths, etc. Smocks/smokkes are chemises, shifts, etc.
So this may indeed be a specialized garment for women to wear in the bath - but for any woman to wear in that setting. For the proper noblewoman bathing in private with her own attendants, it would expose the arms for better washing, and use less fabric than a chemise worn as underclothing. For the Bath-house Babe, this specialized garment would also have the benefit of looking particularly sexy.
