The short answer
Yellowstone’s roads follow a seasonal rhythm. The northern road from Gardiner to Cooke City is open to cars all year. Most other roads open in stages from mid-April through late May and close to regular vehicles in early November, with oversnow tours from mid-December to mid-March.
Spring openings
Openings are staged and weather-dependent. The West Entrance and the roads linking Madison, Old Faithful, Norris and Mammoth typically open in mid-April. The east and south entrances and Dunraven Pass follow through May.
Summer and fall
From late May through mid-October every major road is normally open. High routes close first in fall: Dunraven Pass and the Beartooth Highway typically close by mid-October. Most park roads close to regular vehicles in early November.
Winter
Only the northern road is open to cars. From mid-December to mid-March, guided snowcoach and snowmobile tours from West Yellowstone and Mammoth reach Old Faithful and the canyon.
Which entrance from Bozeman?
Use West Yellowstone (90 miles) for the geyser basins when roads are open, and Gardiner (80 miles) for Mammoth, Lamar Valley and any winter visit.