Yukata
The bathe clothes are the clothes you take with you to bathe with. This is Yukata.
ゆかた
The reading is totally an exception. The reading comes from the meaning, though. Yukata = ゆかた.
彼女は自分の古い考え方にしがみついて、毎晩パジャマの代わりに浴衣を着て過ごした。
She clung to her old ways of thinking and wore a yukata instead of pajamas every night.