Neither of these approaches is completely satisfying, as a one-way loop would imply the existence of physical divider separating the bus terminal from the mainlanes of 87th Street. But it’s hard to place the turning circle as a node without the roadway geometry looking clunky.
Are there examples of this sort of bus turnaround elsewhere? How should they be mapped?
This is not a turnaround, its a left-turn combined with a layby or perhaps Key:bus_bay - OpenStreetMap Wiki that’s larger than usual. Note that a bus coming from the west side could also go there without turning.
As such, I wouldn’t even draw the way beyond the southern highway, and perhaps tag the way appropriately with bus_bay.
Something like this:
Note that I’ve drawn the left turn as a normal junction, which is only necessary since the ways are mapped separately. They aren’t actually separate afaict, though convenience wins here I guess.
It is a turnaround as you can clearly see at the tyre marks on that bulb loop. Buses come from the east, have their own left turn lane there, turn left into the loop, have a stop there and leave into eastern direction afterwards.
Buses coming from the west could also enter there but according to the tyre marks they don’t (at least not regularly). So the purpose of this “bay” is to give enough space for the turnaround, including a stop area.
In all fairness, this is likely an exception to the carriageway rule because the rest of the West 87th Street is apparently divided, just not in that place.