Play Endless Nightmare enough to beat Pyramid Head ("the manager"). He will drop the commissioner's wig which you can then give back to the commissioner the next time you meet him. Pyramid Head for me showed up in 140F (Edit: 100F in v.1.0.6) The commissioner gives the P90 SMG to you as a reward for returning his wig to him.
I'm probably missing a recipe or something, but in 1005 floors, I've not found any way to get more SMG ammo for the P90. All that drops from defeated enemies are ammo for the Glock, the AR, and the shotgun. Ammo for the Desert Eagle at least drops from repeatedly fighting the secret Licker enemy in Power Supply Station area, but I've not found a way for P90 ammo to drop. Yes, it uses its own ammo, named "submachine gun ammo", and uses assault rifle skills, but somehow the game doesn't seem to drop any ammo for the gun. From what I've seen, the merchants don't sell it, either. Maybe it's craftable, but when I checked my crafting list, submachine gun ammo isn't on it.