score:11
Night busses are very rare in Germany. Especially from small cities such as Rutesheim, there are very few options available.
So let's try what we can get.
The following is for random dates since I don't know when you will be travelling.
Apparently, the S-Bahn is still running late from Rutesheim. It can bring you to Stuttgart Hbf or Stuttgart Airport (e.g., starting 00:14 and arriving at the airport at 1:22 or at the train station at 00:42). From the airport, there is a Flixbus running to Karlruhe Central station (02:35 - 03:35). Alternatively, there may be a 02:41-03:47 connection with the ICE from Stuttgart Hbf. All of this does not seem to be a problem.
But when you look at how to get to the airport on a Sunday morning, you will see (with the bahn.de website) that there are simply no busses running so early. Looking at the website of the airport, you will see that there are two bus lines that serve the airport, and both of them do not arrive before 10am on Sundays.
https://www.baden-airpark.de/en/directions-and-parking/arrival-by-rail-and-bus/
So that seems to be the problem that you are having. So you will need to use the taxi for a part of the trip. According to Google Maps, the next train station seems to be "Baden Baden".
Now searching for a night train connection from Rutesheim to Baden Baden, you will see some options that get your there on time.
Upvote:3
A solution using public transport seems really a serious problem at this time of day and with the circumstances described by DCTLib.
That's why I'd recommend a one-way car rental. Using a bigger car rental company like Europcar you could rent a car the day before in Stuttgart (airport for example) and return it at FKB. This should be around 90-100 Euros. You could park it overnight in Rutesheim and then just continue easily in the morning. Should be hassle-free.
Upvote:5
As JΓΆrg and Sebastian already pointed out, the railway line between Rastatt (2nd closest station to FKB airport) and Baden-Baden (closest station) is disrupted until further notice, at least until 7 Oct 2017. There's a rail replacement bus service if you need to get to Baden-Baden. The journey planner at www.bahn.de takes this into account.
If you go by train during the disruption, you might prefer taking a taxi from Rastatt rail station to the airport (about 40 EUR). This would save you some time and another interchange.
If you continue to Baden-Baden rail station, you're closer to the airport and the taxi fare will be lower (about 30 EUR, prices are estimates by www.taxi-rechner.de). You might want to pre-book a taxi with one of the companies mentioned on the airport website and agree on a fixed price.
Of course, considering the taxi fares, it could be worth looking for a different flight from Stuttgart ...