If you're trying to end petrification resulting from something that's not a spell, like a Beholder ray, Dispel Magic won't work. You'll definitely need Greater Restoration for that. It is a spell with a duration, so you can try Dispel Magic on it.

How do you get rid of petrification?

Petrified is a condition, there are currently two spells that remove it. Greater Restoration as mentioned here, and Wish, the 9th level spell. Usually there are also consumables (potions/salves/oils) that will remove petrification, however we have not seen any of those yet (we'll likely see them with the DMG though).

Does dispel magic work on Bag of Holding?

Dispel Magic specifically ends the effects of spells with non-instantaneous effects. So magic items like bag of holding and spell scroll are not effected.