As far as I can see is with one change the easiest, quickest, but not the cheapest the Thalys to Bruxelles-Midi/Brussels-South and from there the direct intercity train to Bruges. Total travelling time is 3.06h and the scheduled time to change trains in Brussels is 18minutes.
Don’t worry too much about missing a train, there are comfy direct trains almost every half hour from Brussels to Bruges. On the map Antwerp lookes quicker, but the train to Bruges takes an half hour longer, total traveltime also depends about the time needed to change trains.
If you book online you don’t have to worry about buying a ticket at the ticketbooth. Be aware that the Thalys ticket will include an EBS, meaning the ticket is also valuable for any further destination in Belgium, in this case Bruges, so one ticket is enough to travel between Amsterdam and Bruges. You can pay with the well-known brands of creditcards.
For more info, booking online see www.belgianrail.be. Select English and under the timetables tab there is a international travel button for the highspeed train from Amsterdam to (Antwerp?)/Brussels.
About the semi-flexible and flexible booking is that once booked you can change things to a certain extend without or (I think few) additional costs. As soon as you travel with the intercity train from Brussels (or still maybe Antwerp) to Bruges is the date that the ticket is valuable is important, taking the next or later trains the same day is no problem. Travelling with the highspeed train, you have to travel on the date and the time indicated on the ticket.
Seen the total amount of travelling costs with 7 persons by train I think a rental minivan for the Amsterdam-Bruges leg is still worth to consider.