Zaltbommel has a train station. Check Dutch railway for schedules and prices.
Once arrived, Zaltbommel is perfectly walkable. You do not need a bus or other transportation.
A train ride from Amsterdam to Zaltbommel (with one change at Utrecht) takes only 1 hour and 8 minutes. A single ticket costs € 11,50 and a return ticket is € 21,10 (prices 2008).
Four trains arrive at Zaltbommel station every hour; two coming from the direction of Utrecht (the stopping train to Den Bosch), the other two coming from Den Bosch (the stopping train to Utrecht). From the station it is about fifteen minutes walking to get to the old town. This is not a pleasant walk. In fact, I found it very unpleasant. For some reason much of it goes through gravel, which was quite a torture to my already suffering feet that day. I think it's worth it, though.