#You would suffocate to death unless it is a short trip.
You would suffocate to death unless it is a short trip.
Bag of Holding:
Breathing creatures inside the bag can survive up to a number of minutes equal to 10 divided by the number of creatures (minimum 1 minute), after which time they begin to suffocate. roll20
Suffocating (emphasis mine):
When a creature runs out of breath or is choking, it can survive for a number of rounds equal to its Constitution modifier (minimum of 1 round). At the start of its next turn, it drops to 0 Hit Points and is dying, and it can’t regain Hit Points or be stabilized until it can breathe again. roll20
Thus, the Periapt of Wound Closure can not stabilize you. You'd have to start making Death Saves after you drop to 0 HP. Unfortunately, three successes can't stabilize you either, so you'd be making Death Saves until you died or could breath.
Note: The PHB errata updated the wording of Suffocating to include that you can not be stabilized.