We started at Crane Flat ... I'd recommend that. There is parking with a gas station that has food and drinks too.
If you go all the way past Tenaya Lake, you should be able to get to the East side. I don't think you can see Mono Lake unless you keep going to the bottom where it intersects US395. But if you do decide to do that, you'll want to check and see if the Whoa Nellie Deli (Mobil Station) is open ... some of the best gourmet food in the Eastern Sierra. And after that, you gotta climb back out, and the climb from the East is steeper than it is from the west.
They should announce the date on that website, but it's not certain. Last year, they didn't open the road up to bikes only at all ... and gave some kind of lame excuse. This year, they just opened it up to the gate on the east side, and for bikes only ... last weekend. But they announced it Friday afternoon(!)
Stay tuned. We're checking it out too, and if we hear anything I'll post something about it here. Maybe you can join us!