Mid to late April is a pretty good guess though by the end of April you likely will not be able to ski the Sherburne trail to the parking lot... But they close it in sections, so you still might be able ski down to, say, 2500ft and have a shorter hike out.
Typically, the full complement of lines in the bowl are available throughout April.
Alternatively, in a good snow year, you can wait till mid-late May, drive up the Auto Road, ski in the snowfields near the summit, then down climb and still have some pretty good snow in the Bowl (typically left gully and sluice are two of the longer lasting runs).