Yes, you can have multiple fighting styles, so long as they are different.
However, as per PnP rules a sword bard can only choose from duelling or two weapon fighting, archery is not available to them (it's College of Swords, not College of Bows).
Damn that just broke my heart. Makes sense though not sure where I got it would be more options. Now I won't get the +2 til character level 7 when I add a Fighter sublevel, and that's 1 less defense