From Basel ... via Fribourg Baden Baden Offenburg Villingen Donaueschingen Singen Waldshut Basel
From Berne at 08:04 to arrive Basel SBB at 08:58 and stay on the same train to the other railway station, Basel Bad. Alternative by auto, parking near the Basel Bad station on the German side of the city.
Basel SBB at 09:04 to Basel Bad railway station then at 09:13 to Freiburg im Breisgau (D) arriving 09:50. Then two hours in Freiburg (or alternatively more time in Baden Baden)
Freiburg im Breisgau (D) ab 11:57 to Baden-Baden an 12:41
From Baden-Baden at 13:30 Offenburg at 13:59 Hausach ab 14:18 Hornberg ab 14:26 Triberg ab 14:39 (time to stop for an hour or two anywhere along this route) St Georgen ab 14:54 Villingen ab 15:04 Donaueschingen ab 15:13 Singen an 15:43 (suggest an hour in Donaueschingen)
Donaueschingen ab 16:18 Immendingen ab 16:29 Engen ab 16:42 Singen an 16:50 Train from Singen at 18:01 Schaffhausen at 18:15 to Erzingen
Erzingen ab 18:29 Tiengen ab 18:37 Waldshut ab 18:42 Bad Säckingen ab 19:06 Basel Bad Bf an 19:17
You can go through Basel to the Swiss railway station by tram, or wait for the train to Bern:
From Basel Bad Bf by rail ab 19:41 to Basel SBB continuing at 20:00 arriving in Bern at 20:56
Trains in Baden-Württemberg on the main routes have a frequency of 1 hour, on the country routes of 2 hours. Check the connections using www.sbb.ch. You can specify a route like Berne via Baden-Baden to Singen, and then check the trains and their stops in detail. Make print copies of the alternatives which are practical.
clickable map of all rail connections
http://www.3-loewen-takt.de/d/2368/
Clickable rails
655 Mannheim
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Biblis 665.1-2 Osterburken-Seckach-Heidelberg-Mannheim700 Karlsruhe-Mannheim702 Offenburg-Basel704 Bruchsal-Germersheim706 Heilbronn-Heidelberg-Mannheim719 Offenburg-Straßburg720 (Karlsruhe-)
Offenburg-Singen-Konstanz727 Freiburg-Titisee-Neustadt-Donaueschingen728 Titisee-Seebrugg730 Basel-Singen731 Friedrichshafen-Singen731 Friedrichshafen-Lindau734 Steinen-Weil
am Rhein735 Basel-Zell
(Wiesental)740 Stuttgart-Singen742 Villingen-Rottweil750 Stuttgart-Ulm751 Ulm-Aulendorf-Friedrichshafen755 Ulm-Sigmaringen-Neustadt757 Aalen-Heidenheim-Ulm760 Stuttgart-Plochingen-Reutlingen-Tübingen766 Sigmaringen-Aulendorf770/710.5 (Stuttgart-)
Bietigheim-Karlsruhe774 Tübingen-Horb-Pforzheim780 Stuttgart-Heilbronn-Würzburg782 Wertheim-Lauda-Bad
Mergentheim-Crailsheim783 Heilbronn-Schwäbisch
Hall-Hessental (-Crailsheim)785 Stuttgart-Backnang-Schwäbisch
Hall-Hessental-Crailsheim786 Stuttgart-Aalen-Crailsheim995 Aalen-Nördlingen