How exactly does the suit come out of his bones?
In "Extremis" it's just the undersheath (a body suit that allows him to connect to the physical armor.) Coming out of the bones isn't too hard, your bones are fairly hollow and porous (to llow for bone marrow to do its thing.) The "idea" is that the undersheath is stored in the "hollows of his bones" after being injected with a variant of the super-soldier serum. The undersheath comes out of the pores of his skin when he wants to release it allowing him better and quicker interaction with the armor and it's various abilities and even giving him a quicker response time and the ability to "think" the actions he wants the suit to make rather than talking to its AI.
In the comic, for example, he's able to instantly think to connect to orbiting satellites and get the information he wants to track a villain (someone else who had taken the "Extremis" serum and is rampaging through the city) instantly in his mind, again, rather than interacting with the AI and HUD inside his suit.