I need advice plsss

Ok so my boyfriend and I have been together for over 3mos now. He’s met my grandma bc that’s who I stay w. So my grandma is really old school so, whenever he comes she expects him to walk up to the door and at least be a gentleman and speak to her as well, but he always acts like he has a problem w doing that like he’s so lazy to get out the car but he does it any ways. He speaks to her and he’s really good at keeping a conversation going and starting one. So today my grandma asked me to ask him if he wanted to go shopping w us and I did and he said No, bc he doesn’t feel comfortable” w my grandma yet. I guess I can understand that, but I told him “Ok but the only way to feel comfortable is too hangout w us and be around her more” and he just said “Next time” but he’s really bad at keeping his word w me sooooo.... So should I be feeling some type of way? Or just let him be when he’s ready? But it just seems like to me he doesn’t want too, and it’s making my grandma think that he just doesn’t want to be around her. Help pls