Simple RAW for Pathfinder Thread VI: Return of the Red Die

[Rynjin]

A379: All creatures follow the same rules on natural healing.

Natural Healing
With a full night’s rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night.

If you undergo complete bed rest for an entire day and night, you recover twice your character level in hit points.

It would be up to GM discretion on whether an Animal Companion's character level corresponds to the Druid's level (since Animal Companion is sort of a "class", they even have archetypes) or their Hit Dice though.