It's crossed my mind before. I always thought she'd likely wear simple, comfortable underwear. I'd imagine the color to be pink or purple, or perhaps white and purple striped to match her daily clothing. I think black would suit her well too.
I'd want her to wear whatever she was most comfortable wearing. I remember reading a theory about her outfit somewhere that said she likely wouldn't wear a bra due to the severity of her asthma. This also seems fairly probable to me, seeing as she's a hikikomori and has long multi layered robes that generally render wardrobe malfunctions a non-issue anyway.