Turn on a multi-functional pressure cooker (such as Instant Pot) and select Saute function; heat until indicator reads 'Hot.' Add bison, onion, red bell pepper, and olive oil. Saute until bison is browned and crumbly, 5 to 7 minutes. Add mushrooms; saute until slightly softened, 1 to 2 minutes.
Stir basil, garlic, oregano, and bay leaf into the bison mixture. Add tomatoes, water, wine, and tomato paste. Turn cooker off. Add pasta; stir until coated. Mix in salt, onion powder, and garlic powder.
Set cooker to Manual. Close and lock the lid. Select high pressure according to manufacturer's instructions; set timer for 5 minutes. Allow 10 to 15 minutes for pressure to build.
Release pressure carefully using the quick-release method according to manufacturer's instructions, about 5 minutes. Unlock and remove lid. Stir well.