The bestshare stat shows exactly that. It resets everytime a block is found on the pool. The bestever stat is the bestshare you ever found and isn't reset.
It doesn't exactly; It shows the bestshare overall in this latest stint of trying to find a block since the last solved block. I would like to see the best share I have submitted on this round of work. When the block is solved, be it by the solo pool or another pool, this data resets.