I found getting from Baden-Baden Airport (Karlsruhe-Baden) to Baden-Baden town a little tricky so here's some help.
When leaving the airport take Bus 205 signed to Baden-Baden, this takes you to Baden-Baden train station (Bahnhof Baden-Baden) not the town centre. Here change to Bus 201 to Leopoldsplatz which will take you to Baden-Baden itself (for Caracalla-Therme/ Friedrichsbad Spa etc).
Bus 205 (or any airport express) doesn't run on a Sunday however, so you have to take a taxi from Bahnhof Baden-Baden to the Airport - be warned (around 30 Euros).
It's worth printing this bus map out before you go to avoid an hour or so of confusion like I had.
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