I had another browse through some Bierstadt paintings and I was wrong — there is a painting with Half Dome in it, although it’s not exactly a painting OF Half Dome:
It’s called, appropriately enough, The Domes of the Yosemite. I believe this is a view from the top of lower Yosemite Falls, with the upper falls on the left (although we didn’t go up there; the falls were dry). It’s somewhere between this view (Washington Column on the left, guess who on the right):
and Tunnel View (this is the first view of the valley you get driving in):
You have to imagine you’re down the valley and around the corner from El Cap (on the left).
Comparing the Bierstadt view to the topo map, I believe the point jutting over the left side of the valley is Washington Column, the round dome between it and the falls is North Dome, and the sliced-off round place directly in front of North Dome is Royal Arches. I think the largest dome on the right is Half Dome — it doesn’t quite look like it, but there have been massive rock falls from the face since Bierstadt was there, so I think the rock in front of what appears to be Half Dome just isn’t there any more. My best guess.
And by the way, I’m working on a chart of “The Domes of the Yosemite”.