Set ice cream out to soften. Meanwhile, in a large skillet, heat butter, sugar, and rum over medium-low. Cook, stirring occasionally, until smooth and bubbly, 4 to 6 minutes.
Add bananas, and cook, gently swirling skillet, until bananas are just warmed through, 1 to 2 minutes. Scoop ice cream into bowls, and top with bananas and caramel sauce. Serve immediately.