The drive between Yellowstone and Glacier is between 10 and 12 hours. Directions are available here.

We'd recommend making the trip in two days, since there's lots to see along the way in cities like Bozeman, Butte and Missoula!

I did this drive in the summer of 2008. I drove from Glacier to Yellowstone. I was quite surprised at the distance, and the time it took to cover all those miles (about 400 total).

I left Glacier in the afternoon, after having explored the area at the top of Logan Pass during the day. I was able to make it to Missoula that evening and stayed at a hotel. I liked Missoula because it is right on I-90, which is a main interstate.

The next day I drove along I-90 to a point just west of Bozeman, and then drove south on 191 to West Yellowstone. I arrived in the afternoon, in time to grab some dinner, and set up a campsite just outside of town along the Madison River.

I guess it is possible to drive that whole distance in one day, but for your sanity I'd suggest breaking that trip into two days.