Welcome, Kr1sh!
When you write, "food & gas resupply at Bishop Pass Tr jn (RS)", do you mean someone BRING your resupply over Bishop Pass down to the trail junction?
If that is what you mean, then it is pretty difficult. You could hire a packer to bring it in, but would likely cost you over $500, since you pay for packer, his horse, and a mule. And they are very reluctant to do a hiker resupply, due to the logistics -- what if you aren't there when you said you would be? They cannot drop the resupply and leave.
So that leaves you with the option Bob talked about above: hiking out, hitching into Bishop, shopping, then returning. But that Bishop Pass exit is a 4000' climb out of the canyon! It would take you two days to go out and return.
JMT hikers usually resupply at Edison Lake (VVR --Vermillion Valley Resort) or Muir Trail Ranch, just one day south of VVR. Both have access from the west, and both will accept resupply packages shipped into them. No animal stock required.
I am not sure what you mean by "Kearsarge first lake CG", but it looks like you are looking to get a resupply over Kearsarge Pass. That one is a little easier, but still expensive. I believe the packers out of Onion Valley will charge something like $200 to bring a resupply into the Charlotte Lake Ranger Station, and the ranger there in the past has agreed to keep resupply packages for a short time for hikers. Not absolutely sure of this, though.
It would take about a full day to hike out over Kearsarge, hitch down from Onion Valley to Independence, and return. That might be your best option for the second resupply.
Sure hope this helps!
