YNP rangers are very serious about anything to do with outside cooking and eating. If you leave a cooler out or picnic supplies or a grill, they will swoop in and confiscate it unless you are eating or actively moving to get them contained. And then you get fined! We had a ranger stop in front of my camper to make sure I was putting all our stuff away properly and he didn't leave until every last thing was secured.
If you don't have a place for your grill, see if it will fit in one of the many steel bear boxes. I'd be a little leery about put a yummy smelling grill and leftover ashes inside my truck bed. Bears can easily open trunks and car doors to get to food. I would think a truck would be only slightly more difficult for a determined bear.