Suppose Deadpool was shot and the bullet stays in his body. What will happen to the bullet? Would Deadpool remove them? Or would be be left behind?
I'm not sure I saw such thing in the movie. But we know he has a strong healing factor. When he cut off his hand to let himself free from Colossus' handcuff, we sam him grow a baby hand. That implies he has regeneration powers.
In comics, it is not only the bullets that impales him.
In these moments, I hardly think he waits until the object inside removes itself/pops outside from his body.
If the object is small enough like a bullet or he has more than one object impaled, he lets it pop out or maybe he doesn't realise that he has a bullet in him. He removes what he can remove and lets the others find a way out.
His regeneration ability is very strong and providing in these cases.
Sorry about the blood and guts. Literally.