yes they do.
seats are limited so sign your group up the night before.
do this at the concierge desk in your hotel lobby.
you can choose one of 2 times for the morning run.
they evening return trip back to the hotels is around when sw closes.
some do not want to wait that long and have taken taxis back to the hotel.
you do circulate to the other hotels before going to sw.
each hotel does not have it's own bus.
at hrh the sw shuttle bus is on ground floor at the end of the building.
you can get precise info on that location from the front desk.
depending on when you go to sw, times might be different than what i listed above.