What is the best, most economical way to travel by train from Bruges to Amsterdam? Thank you.
There are two options, explained fully and with links to the websites where you would buy the tickets, on The Man in Seat 61: http://www.seat61.com/Europe-train-tickets.htm#Brussels-Amsterdam
The best way is to buy in advance a Thalys ticket for the Antwerpen-Amsterdam sector, then a regional ticket on the day of travel Brugge-Antwerpen (there are trains every 30 min for the latter).
Define "best". Depending on your priorities, "best" might not equal "most economical."