"What do you think of the Terra Nova Bothy Bag, for when you don't have a tent along?"
I've never taken a tent, sleeping bag, or bivvy sack on Whitney, so I don't exactly see the point. In the 36 times that I've been up there, I have been snowed or sleeted upon maybe three times. Then add a brief rain shower another three times. I'm not sure that I would want to hunker down and wait for that sort of weather.
If you carried something like that, it would be another pound in your daypack. Frankly, my daypack is ready to burst at the seams as it is.
If you carried something like that, you would deploy it either on the way up, on the summit, or on the way down. I can't imagine deploying it on the way up, because it is very rare for there to be serious weather early in the day before sunrise. I can't imagine deploying it on or near the summit, because that is a very bad place to wait out a storm. I can't imagine deploying it on the way down, because I am so tired that I just want to get down to the campground and relax, and I would likely want to plow down despite rising water. There are a half-dozen bivvy sites on the bottom few miles, mostly around big boulders.
I have gone up when the weather was iffy, so I made the run up the last two miles while holding my breath almost. I touched the summit hut, signed in on the register, and then went down immediately.
So, no, I don't carry emergency shelter. What I do carry is a handful of Esbit tablets and a titanium cup. If I had to hole up someplace at night with my rain suit on, some hot water or Gatorade might make it easier.