Combine bread crumbs, onion, ginger, mustard, salt, and curry powder together in a bowl; add ground bison, oats, and eggs and mix well. Form bison mixture into 4 patties.
Heat olive oil in a skillet over medium heat; cook patties until evenly browned, about 5 minutes per side. An instant-read thermometer inserted into the center should read at least 160 degrees F (70 degrees C). Transfer burgers to a plate to cool completely.
Bring a large pot of lightly salted water to a boil; cook the rotini at a boil until tender yet firm to the bite, about 8 minutes; drain and transfer pasta to a 1 1/2-quart casserole dish.
Preheat oven to 375 degrees F (190 degrees C).
Spread tomatoes and tomato sauce over pasta; sprinkle 1/2 the Cheddar cheese over tomatoes. Arrange burgers on top of tomatoes and sprinkle the remaining cheese over burgers and tomatoes.
Bake in the preheated oven until cheese is melted and tomato sauce is bubbling, about 30 minutes.