Not sure, but I think some of the Mountaineers Route permits are available ONLY on a walk-in basis. You can call the ranger station and ask. When you get a wilderness permit, it is good for as many nights as you want to go -- you don't get a new permit for each day.
As for setting up a bivy sack and camping, if you are out in the woods, nobody cares. I have camped like that numerous times. If you are in someone else's camp site or in view of the road, it matters. I have camped in parking lots (setup late, get up early) in the past, and there was no problem. However, around Whitney Portal, I am just not sure where you could find enough level ground for a bivy that wasn't already in use as a camping area.