It all depends on your level of conditioning and how well you are acclimated. If you've never hiked at that altitude before then I wouldn't worry about setting a speed goal but rather just getting up and down safely.
I like to start around 1:30 to 2:00 am. I'm from the Bay Area as well and getting down earlier allows me to drive home the same day (although it's not an easy drive of course).
I would do a practice hike in Yosemite like Clouds Rest, or perhaps Granite Pass in Kings Canyon. Both of those hikes mimic the elevation gain and distance and will give you some practice at training at altitude (although at a lower altitude).
Also I would recommend spending a night at Mammoth Mountain Inn along the way. It only 10 minutes off of 395 and AFAIK it's the highest full service hotel in California at 9000 feet. Then in the morning it's a 2 hour drive to Lone Pine to pick up your permit and spend the day acclimating further at the Portal campground. It makes a huge difference to acclimate a full extra day.
Last edited by bruce; 07/23/17 06:59 AM.