Anyone know if all the mountain bothies (http://www.mountainbothies.org.uk/locationmap.asp) in Scotland, Wales and northern Ireland are already on osm?
The answer to “are all the X in OSM” is almost always “no” because there are almost always some that haven’t been surveyed; or whose status has changed since they last were, whatever the “X” is 
If you’re proposing to import anything into OSM from a third-party source you’ll want to read https://wiki.openstreetmap.org/wiki/Import and follow https://wiki.openstreetmap.org/wiki/Import/Guidelines . Unfortunately, “lists of things found on the Internet” are often encumbered by licence problems because of whatever was used to obtain the location for the list, though in this case I suspect that that might be less of an issue.
I’m not sure that alpine_hut is really correct for mountain bothies: most places so tagged in UK are huts belonging to the senior climbing clubs which although not open to non-members definitely belong to the tradition of alpine huts.
The one up the strath from Sandwood Bay is mapped with tourism=wilderness_hut, so a revised overpass query is http://overpass-turbo.eu/s/nGL which gives 110 altogether, 79 shown as run by the MBA (see http://overpass-turbo.eu/s/nGM)). i’d presume this is a decent proportion of the total.