I believe the route from the U-notch (west side) is clear of snow, I was just there a few days ago. If we are talking about the same place, you'll want to cross Thunderbolt Pass on your way to Bishop Pass. T-bolt pass isn't marked on a lot of maps, but it's essentially the small ridge that comes out west from T-bolt peak, you'll know what I mean when you see it.
Last week some friends did the traverse from T-bolt to Polemonium with one car from the glacier lodge T/H. If you get an early enough start and are fast enough you can make it in and out in one day
Of course this entails climbing a route on the east side, perhaps the underhill couloir, which isn't bad at all if you're comfortable with 4th class (and you obviously are if you're doing this traverse
Hope this helps, maybe I misunderstood your question, in which case I apologize