They don't but you can get Super Shuttle, UBER or take the BART to Embarcadero and a cab from there.
I'm pretty certain that there is not a shuttle service to/from the airport. For trips in and around the city public trans is great. In fact the bus stop is right in front of the hotel. If going to the airport I'd suggest using a rideshare service like Uber.
Get an answer from Suites at Fisherman's Wharf staff and past guests.