I was sleepy, so I went to bed.

Literal

Sleepy was [because-ので] bed [dative-に] attached.

床につく is a set phrase meaning 'go to bed' — literally 'attach to the bed/floor.' 床 (とこ, not ゆか here) refers to a traditional Japanese bed or sleeping pallet. An elegantly literary way to say 'went to sleep.'