A sleep bed is where you sleep. Where do you sleep? In a bed or a crib. Side note, if you're a baby sleeping in a crib, you must really want to learn kanji.
This word uses the kun'yomi readings of the kanji. You didn't learn the second kun'yomi reading for 床. You take とこ and rendaku it into どこ. How do you remember this? Just think about your bed. Then wonder, "where (どこ) is it?"
"Come now, isn’t it about time for bed?" My grandfather used to say that to me every night.