Over her clothes

The fabric seemed transparent enough that she'd not dare to wear it over her underwear.
She started looking for the hole for the head, but it didn't appear to be one. The whole outfit seemed to have only one hole at the bottom and really wasn't much more than an oversized pillowcase.

Lauren was about to return the costume but decided to put it on ant try anyway. She threw the sheet over her head and let it fall to her feet.
Then looked at the mirror and let out a gasp of surprise. Not only the fabric was semi-transparent. Herself was semi-transparent too! She could clearly see the wallpaper pattern behind her!

Looking closer Her clothes became indistinguishable and really only added a bit of colour to otherwise glimmery-white silhouette. The contours of her costume seemed smoky and ill-defined.

A bit shocked by the effect she wanted to talk to the owner. She tried to move the curtain to the dressing only to find her hand go through it.
"This costume must be messing with my depth perception" she though.
Indeed her eyesight was slightly obscured by the hood that did not have any eye-holes.

She tried again this time with greater success.