Estimates by Travis5152 are reasonable. Two wrinkles:
1. The drive will "feel" a helluva lot longer because the last 17 miles of that road are brutally rough.
2. Doing White Mt. in a day from Orange County seems needlessly grueling to me. Why not camp one night? Also, make no mistake about the fact that the White Mt. hike is deceptively tough - mostly due to altitude. If you've got some experience with 14,000-foot hikes, and you know your body will adapt just fine, I think your plan could work. But it's entirely possible that doing White Mt. in a day from Orange could turn out to be just plain miserable.
Good luck!