Reproducible using creative to get the bed item. Then switch to adventure.
1. Place the bed
2. Try to remove
Minecraftwiki says it can be broken w/ any tool.
Linked issues
Comments
It doesn't work with any of:
1. Sword
2. Axe
3. Shovel
4. Pickaxe

Confirmed.
No tool, sword or hand can destroy a bed.

Resolved as duplicate of MC-2789 - there are all unbreakable blocks summarized.
Adventure mode is different, you need the assigned tool. Since the bed is wood, you'll need an axe.