@Nigel, you posted while I was typing.
The deal for free transfer to the hotel is described here. It requires "a room reservation confirmation stamped with “Mobility Ticket.”". It is valid from the airport or station, but not, AFAIK, from either of the boat terminals. The OP would probably have got away with it if they had a printed confirmation, but I was just being safe and saying he should get a ticket it is only CHF 3,40!
I am assuming the hotel is at the Bahnhof SBB, not Badischer Bahnhof, as there are lots of hotels at the former and only one at the latter. "Gare SNCF"* is next to Bahnhof SBB, same tram stop. When the trams arrive there they make an announcement in 3 languages:
"Bahnhof SBB SNCF, Gare CFF SNCF, Swiss and French Railway station"