Ammunition warehouses detonating after a UAV attack in Toropets, Tver region of Russia.

Probably not, but definitely rockets and missiles.

Bullets don't have much energy unless the explosion is contained/directed inside a barrel. Here is a firefighting demonstration on how to deal with burning ammo. The tl;dw is: just make sure you are wearing the facemask and other insulated clothing so you don't catch one in the eye, but they are otherwise harmless.

Also, as Wileshire mentioned: larger things like rockets and missiles can be dangerous still as the rocket motor can ignite, and send the whole thing at high speed to nearby areas.