As with most towns in this corner of Switzerland, Bulle (as of 2010) lacks a 100% veg restaurant and, sadly, at most places there are few if any veg options and often nothing at all for vegans. (Bulle's veg-friendly offerings are essentially limited to either Asian food or felafel/hummus at one of the kebab joints.)
Le Tresor des Cinq Epices (The Treasury of the Five Spices) offers by far the best experience in town for veg*ans in terms of variety, taste, quality, and atmosphere. The Asian fusion menu is well-balanced and, with about 10 vegan options, provides ample variety to satisfy most diners. Vietnamese, Chinese, Thai, Cambodian, Japanese, and Indian cuisines all make appearances on the menu and the specials board. The Vegetarian Combo Plate (with spring rolls, samosas, and other tasty bites) is highly recommended as an appetizer. The veggie sushi is quite nice, as are the curries. And they have vegan sorbet for those with sweet teeth. :-)
Note that the menu is in French, but both the owners speak good English. Just be sure to tell them if you're vegetarian or vegan and they should take good care of you.
In case you'd like to check the menu, their website is http://tresorcinqepices.host22.com/