Just to be sure I understand your question, the cruise ends at 9 in the morning in Basel but your flight doesn't take off until 6 that evening? Sadly I'm afraid you may have a very long day hanging at the airport.
We've been on 1 previous Tauck river cruise and this is how the departure at the end of the cruise worked. The Cruise Director (CD) will ask at the beginning of the cruise for you to confirm your departure plans. Then the second to last day of the cruise, they will give you a group assignment number with special tags for your baggage. The number of different groups depends on the different times and places people need to be e.g. some people have early flights, some are going to the train station, some may be staying on in Basel at the Tauck hotel, etc. Those with earliest departures will be in the first group and so on down the list. You will likely be in the last. They'll also tell you what time to have your luggage outside your stateroom. The staff will pick it up and take it out to the vehicle transporting you. Once you get to the airport, you take your bag from there and you're on your own. Breakfast times will be adjusted on the ship depending on departures.
When are you taking this cruise? We're on the 14 Oct departure from Amsterdam.
You should call Tauck. They may have hotel for people that extend stay and will be willing to keep your luggage for you. Not much to do at the airport. You don't want to hang out all day.
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We've been on 1 previous Tauck river cruise and this is how the departure at the end of the cruise worked. The Cruise Director (CD) will ask at the beginning of the cruise for you to confirm your departure plans. Then the second to last day of the cruise, they will give you a group assignment number with special tags for your baggage. The number of different groups depends on the different times and places people need to be e.g. some people have early flights, some are going to the train station, some may be staying on in Basel at the Tauck hotel, etc. Those with earliest departures will be in the first group and so on down the list. You will likely be in the last. They'll also tell you what time to have your luggage outside your stateroom. The staff will pick it up and take it out to the vehicle transporting you. Once you get to the airport, you take your bag from there and you're on your own. Breakfast times will be adjusted on the ship depending on departures.
When are you taking this cruise? We're on the 14 Oct departure from Amsterdam.