Turn on a multi-functional pressure cooker (such as Instant Pot®). Add water, broccoli, green onions, cream cheese, butter, salt, and pepper. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 1 minute. Allow 10 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove the lid.
Using a potato masher, mash mixture to desired consistency. Add Cheddar cheese and bacon. Stir until cheese is melted.