Yes, you have to go via Brussels Midi and get the Eurostar. I'd say it's a no-brainer to take the train if you're headed to London.
I'd book directly through
http://www.eurostar.com/ - the way it works for intra-Belgian connections is that you buy an 'Any Belgian Station' ticket to London, which includes the cost of the connection from anywhere in the country. You're then also protected if your connecting service is late. You need to present yourself at check-in 30 minutes before departure, and there's a recommended transfer time of 20 minutes at Brussels Midi, so make sure there's a minimum of 50 minutes between your arrival at Brussels Midi and your Eurostar departure.
For times of domestic trains from Bruges to Brussels, have a look at
http://www.belgianrail.be/en - they will also let you book Eurostar tickets, FWIW.
There's generally 3 fast trains an hour from Bruges to Brussels, taking around an hour. For avoidance of doubt, Bruges is in a Dutch-speaking area, where it's known as Brugge. You want the station known as 'Brugge', not the branch line station of 'Brugge-Sint-Pieter'. Brussels is a bilingual area, and so Brussels Midi station (for some reason, we call it 'Midi' in English, rather than 'South') is referred to as Bruxelles-Midi and Brussel-Zuid. Trains from Bruges to Brussels generally go through the city to end up at destinations like Eupen, Genk and the Airport. Watch out for the slow train via Torhout that takes over 2 hours!