my son also just turn 4 months yesterday and we've been feeding him when he lie down with pillow. after feed then just sit him and burp or just carry him upright to burp.
He also starting to hold the bottle now with both hand but then after awhile he would bring the bottle out of his mouth or shift to the side of his mouth. what i will do is to correct him by holding his hands to let him suck correctly again. but sometimes he's lazy and just hold my fingers instead.