There are pleny of skiable routes in the bowl. I skied last year the weekend before memorial day and it had less snow than in the picture in the above post. We skied THE LEFT GULLY and THE CHUTE. I am heading up in May for some turns. The drive sucks, but it is well worth it for the experience.
Two sites to check:
www.tuckerman.org - They update the avalanche report daily through the end of may.
http://www.timefortuckerman.com/
LEGEND
1 - Left Gulley
2 - Chute Variation South
3 - The Chute
4 - Chute Variation North
5 - Center Gully South
6 - Center Gully North
7 - The Icefall
8 - The Lip
9 - The Sluice
10 - Right Gully (Lobster Claw, Lion Head Gully 1 2 & 3 further over)