Hello, we are a family of three planning a 15 day trip with Bonn as our base. We would like to explore Amsterdam, Ghent, and Bruges on this trip. We don't plan to drive and would rather take the train or travel by coach. Some possible itinerary ideas would be appreciated. Thanks a lot.

Moved from Travel Tips to Europe and tagged for three countries

from Koeln you have direct train to Bruxelles (thalys) and the same thalys goes from bxl to Amsterdam. Reserve 3 months in advance for best price on thalys site or dB site.
From Amsterdam to Bonn no idea. But dB site will tell you. Very easy and handy site.

From bruxelles you take any train to Bruges or Anvers or Gand. Just. It tour ticket st the trainstation.

Anvers = Antwerpen = Antwerp
Gand = Gent = Ghent

Which month, which winter?
The title says "Winter in Germany" and you are staying in Bonn, but the only destinations mentioned are in other countries more than 3 hours one-way by train from Bonn.
Are you visiting places in Germany? If not, why staying in Bonn when visiting Belgium and Netherlands? If you are visiting during the Christmas season, Christmas markets are possible destinations if this is an area of interest. Otherwise, we don't know what you are looking for in the "winter.".

Bonn is not a good "base" for Amsterdam. It'll take you over 3 hours to get there.
Why Bonn at all?

Perhaps they have family or friends there to stay with?

Anyway - how about some of the many places of interest which are closer to Bonn, within sensible day trip distance? These three cities are too far for my taste.

Cologne, and in The Netherlands, Maastricht would be doable. Aachen of course. Koblenz could be nice and of course the Eiffel region.

you might go to marmelade factory in Bonn.
In Amsterdam must have is to taste "herring" and maybe to check Eindhoven