I have always found the rangers at the Bishop Ranger Station extremely helpful.
There is a lot of info on the web about the hike. Look at some of the peak summiting sites.
I did it years ago and no longer have the links. But there is a good section on White Mtn in Gary Suttle’s book California County Summits which you can find many places on the web used. The only tricky part I recall about the trailhead is that it moves, meaning that in certain parts of the year there is parking a bit further up because the observatory is holding an event.
There is also a section on White Mountain in the Sierra Club book that covers the Great Basin ranges.
You don’t say where you plan to camp. We camped at Grandview. Not a marmot in sight but the birds did peck holes in some of our plastic water containers. Most of the USFS car camping sites did not have water so we hauled it in.
Most of the hike is an old jeep trail and not too steep but you are climbing all the time. I doubt that there is much snow below 10K feet. If the road is open, you could just drive to the TH and then hike until you cannot. BTW White Mtn is a common training hike for folks attempting Mt Whitney. So you could post the same question on the Whitney Portal Message Boards.
The views from the top are awesome. While you are at it, you should also do Boundary Peak. It is a bit more scrambling especially on the way down. The Bishop Range station has a handout that explains the drive on USFS roads to the main TH for Boundary. You most likely will see wild mustangs on the way up or down.
And when you are driving on SR395 you might find your self asking the question why is Montgomery Peak white and White Mtn not white.
Cheers
