If you plan to be resupplied by Raindow Pack station, near South Lake, you'd better contact them. Their corral and tack barn was destroyed by heavy snow and an avalanche. They've just finished digging everything out, and are preparing to rebuild the destroyed structures. They hope to be ready for full operation by the end of June.
However, it is not likely that any packers will be able to cross Bishop Pass this month. There was still an average of 6 feet of snow at the Bishop Lake sensor station, which is about 600 feet below the top of the pass. The South Lake trailhead, as of today, still has a little snow. Mid July looks about right for stock access over the pass. It's going to be a short mule packing season this year in the Eastern Sierra Nevada.