Bring water and quinoa to a boil in a saucepan. Reduce heat to medium-low, cover, and simmer until quinoa is tender and water has been absorbed, 15 to 20 minutes.
While quinoa cooks, mix black beans, red bell pepper, spinach, barbeque sauce, garlic, cumin, and cayenne pepper together in a saucepan over medium heat; add Cheddar cheese. Cook the bean mixture, stirring occasionally, until the cheese is completely melted, 5 to 10 minutes.
Stir cooked quinoa into the bean mixture; spoon filling in a line across the middle of a tortilla. Fold opposing edges of the tortilla to overlap the filling. Roll 1 of the opposing edges around the filling like a burrito.