You are absolutely correct... item BMW3S12 on our website is the same hitch as item BMW3S30-BR. 3S12 just adds the wiring harness.
With either one, you will also need a bike-rack connector or a ball mount. The 2 inch detachable bike-rack connector would be perfect for the rack in your picture. Here is a photo of the bike rack connector. It pushes up from below into the hidden invisihitch receiver and it latches securely in place automatically without a pin. Carrying capacity is way above what you will need for your SportRack and bike.