Tioga Pass is usually the last pass to open for the summer in the central Sierra Nevada. In general, Monitor Pass is the first to reopen, followed by Ebbets Pass and then Sonora Pass.
The opening of Tioga is a coordinated effort between the National Parks Service for the Yosemite portion and CalTrans for the road east of the park entrance. I know for a fact that after last year's winter there was a large avalanche concern around Olmstead Point, so even though the road had been plowed, they kept the highway closed until they were satisfied that there was no risk of avalanche.
SR270 to Bodie is also closed for the winter, but I think it is usually opened in time for Memorial Day.
A lot will have to do with any late season storms that may blow into California. Keep watching road conditions on the CalTrans website for current information as your departure date draws near. Sometimes the online newspaper for Mono County has the estimated reopening date for Tioga Pass.
The others are correct that you will be able to make it from Groveland across Tioga Pass and into Lee Vining. You do have a nice ascent north of Lee Vining to Conway Summit, and then it is mostly downhill from there to Topaz. But you ought to be able to make it from Groveland to Topaz without stopping if you monitor your speed although I have not made that trip yet.
I have crossed the Sierra westbound in our 85 and made it home comfortably to Fresno from Minden NV without stopping. But that leg is mostly a long, steady downhill, and I know the short cuts.