Preheat oven to 350 degrees F (175 degrees C). Grease a baking sheet.
Heat olive oil in a skillet over medium heat; cook and stir onion, red bell pepper, and mushrooms until tender, 5 to 10 minutes. Add diced tomatoes; cook and stir until heated through, 2 to 3 minutes. Combine vegetable mixture and chicken in a large bowl; add barbeque sauce and mix well.
Spread pizza crust onto the prepared baking sheet. Spoon barbeque sauce mixture over crust and top with cheese blend.
Bake in the preheated oven until cheese is bubbling and melted, 13 to 18 minutes.