Bide stops when the Pokémon faints and uses a Reviver Seed
So, I tested this with Pachirisu. I had Pachirisu use Bide against a Pokémon stronger than it. (In this case, Cherrim) Cherrim attacked Pachirisu by using Petal Dance, causing Pachirisu to faint and use a Reviver Seed. Cherrim still kept using Petal Dance, and when I was revived, it didn't say the message "Pachirisu is storing energy."
Also, let's say I used Bide, and Cherrim made me faint by using Take Down, which actually happened. (When you use Bide, you can't move.) Since Bide would make me unable to move, when I was revived by the Reviver Seed, I was able to move.
Therefore, you stop using Bide when the Pokémon using Bide faints and is revived using a Reviver Seed. Hope this helps!