In a 1- to 1 1/2-quart pan over medium heat, melt butter. Add olive oil, garlic, and anchovies; stir until mixture is bubbling.
Meanwhile, arrange vegetables on a platter and baguette slices in a bowl.
Pour bagna cauda into a 1 1/2- to 2-cup fondue pot and set over a candle or medium-low alcohol or canned-heat flame (see notes); stir mixture often and adjust heat as needed so garlic doesn't burn. Serve with vegetables and baguette slices.