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®). 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.