The Clemens party left Heidelberg on 23 July 1878 and proceeded to Baden-Baden, where they would meet Joe Twichell on 1 August.
Twain hired the portier of the Schloss Hotel, Georg Burk, as courier for $55/month and expenses and departed Heildelberg by train for Baden.
There are two possible railway lines that could have been used for this trip:
The Mannheim–Karlsruhe–Basel railway is a double-track electrified mainline railway in the German state of Baden-Württemberg. It runs from Mannheim via Heidelberg, Bruchsal, Karlsruhe, Rastatt, Baden-Baden, Offenburg and Freiburg to Basel, Switzerland. It is also known as the Rhine Valley Railway (German: Rheintalbahn) or the Upper Rhine Railway (Oberrheinbahn).
The line was built as part of the Baden Mainline (Badische Hauptbahn). Between Mannheim and Rastatt it runs parallel to the Baden Rhine Railway (Rheinbahn).
The Rhine Railway (German: Rheinbahn) is a railway line in the German state of Baden-Württemberg, running from Mannheim via Karlsruhe to Rastatt, partly built as a strategic railway and formerly continuing to Haguenau in Alsace, now in France.
It was opened in 1870 as an alternative to the Baden Mainline and runs mostly broadly parallel with the Rhine Valley Railway, which runs from Mannheim to Heidelberg, Karlsruhe, Rastatt, Offenburg and Basel. The Rhine Railway originally ran from Graben-Neudorf to Karlsruhe via a more westerly route than the current route, which is now named the Hardt Railway and is partly used by lines S 1 and S 11 of the Karlsruhe Stadtbahn. In 1895 the current route was opened to Karlsruhe and extended to Rastatt and Haguenau. The section over the border along the Rhine in France was closed in 1966.
See Bædeker The Rhine From Rotterdam to Constance (1878) Route 43 From Heidelberg to Baden page 268