you can do it, but in Montana, Idaho and Wyoming there isn't a density of roads & highways like you might be used to. this means you have to drive indirectly there, and the trip is MUCH longer than crow flight mileage.
south from Bridger to Jackson, cross Teton Pass and keep heading west to Driggs, ID. From the middle of the tiny town of Driggs, head north up the road to Alta, WY where Grand Targhee sits.
nolo and/or rio would know the driving times. I've driven from north-central WY to Targhee and it was quite a trek, but if you do it during the day the vistas will keep your mind happy and distracted.