While the bomber doesn't make an appearance in singleplayer, the B-2 appears in multiplayer as the Stealth Bomberkillstreak for all sides, a 9 killstreak which carpet bombs a large portion of the map. During the bombing, the plane doesn't appear on enemy radar, but is very loud.
The B-2 Spirit appears briefly at the end of the mission "End of the Line", when large B-2 bomber squadron (call sign: Arclight) release their payload and destroy the Federation orbital-weapons factory.
Another look at the Stealth Bomber.
B-2s cannot be shot down at any point in-game. However, an EMP can stop it from dropping bombs mid-run in Modern Warfare 2. This changes in Modern Warfare 3, where the B-2 will be destroyed when an enemy EMP is detonated.
When watching a killcam with a B-2, the player will notice that the top of the plane is very low quality. The cockpit and other physical parts are just textures, with the top of the aircraft being mostly smooth and slightly angled to give off the illusion of a pilot.