Go to http://www.b-rail.be/main/E/
Type place of departure (for instance Namur) and Bouillon in the appropriate boxes.
Instead of 'Station /Stop' select 'All types' for both towns.
Then hit Search.
In the next window, under 'Products', select 'All products'
Then hit Confirm
The result is:
you take a train from Namur (aka Namen) to Libramont.
From Libramont you take bus 8, direction BOUILLON Pont De Germauchamps [TEC]. You stop is called 'Auberge d'Alsace'.
It's a 2 hr, 16 minute trip.
Auberge d'Alsace is just on the edge of the center (I stayed at the Best Western, across the road).
If you're staying just for the day it may be possible to leave your luggage at the Tourist Office. It's in the middle of town, along the river. See photo:
What you do is cross the first bridge you see (essentially means turning right) and walk down the steps, right along the river. You pass an empty space (car/motorhome park) and you'll see the glass building as in the photo above).
Or possibly you may leave your luggage at the Auberge d'Alsace (http://www.aubergedalsace.be/). That would be easiest since that's your busstop. If you take a drink or possibly a meal there, they may be even more inclined :-)
You can then stay at the same side of the river, walk along the Quai du Remparts and follow the signs up to the fortress castle.
Personally I'd stay one night. Just to give you ample time to visit the castle and walk about the little town.
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23, rue Au-dessus de la Ville, (formerly Auberge du Panorama), Bouillon, 6830, Belgium
Good for: Families