Combine mayonnaise, sour cream, 4 tablespoons Parmesan cheese, horseradish, and dill in a large bowl. Add asparagus and stir to combine. Transfer mixture to a round 1.6-liter casserole dish (approximately 7 1/2 inches) and cover with foil.
Turn on a multi-functional pressure cooker (such as Instant Pot(R)). Place the trivet inside and add water. Place casserole dish on top of the trivet. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 1 minute. Allow 5 to 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. Let sit for 2 minutes. Using pot holders, remove the casserole dish and uncover.
Combine remaining 2 tablespoons Parmesan cheese and bread crumbs in a small bowl. Sprinkle mixture over the asparagus.
Set an oven rack about 6 inches from the heat source and preheat the oven's broiler to low. Broil asparagus until breadcrumbs are starting to brown, about 5 minutes.
