In this paper, the design flexibility of the control-bounded analog-to-digital converter principle is demonstrated by considering band-pass analog-to-digital conversion. We show how a low-pass control-bounded analog-to-digital converter can be translated into a band-pass version where the guaranteed stability, converter bandwidth, and signal-to-noise ratio are preserved while the center frequency for conversion can be positioned freely. The proposed converter is validated with behavioral simulations for a variety of filter orders, notch-filter frequencies, and oversampling ratios. Finally, robustness against component variations is demonstrated by Monte Carlo simulations.