The escalating issue of antibiotic resistance in bacteria necessitates innovative detection methods to identify resistance mechanisms promptly. In this study, we present a novel approach for detecting resistance in \textit{Pseudomonas aeruginosa}, a bacterium known for its metallo-beta-lactamase production during the development of antibiotic resistance. We have designed an aptasensor employing Förster resonance energy transfer utilising two distinct methodologies. Initially, indium phosphide quantum dots with a zinc sulphide shell, and gold nanoparticles were utilised as the Förster resonance energy transfer donor-acceptor pair. Although this system demonstrated a response, the efficiency was low. Subsequently, optimisation involved relocating the donor and acceptor in close proximity and incorporating two quantum dots with varying emission wavelengths as the acceptor and donor. This optimisation significantly enhanced the Förster resonance efficiency, resulting in a novel method for detecting metallo-$\beta$-lactamase. Förster resonance energy transfer efficiency was increased from 31% to 63% by optimising the distance and donor using a quantum dot-quantum dot pair. Our findings showcase a cheap, rapid and versatile aptasensor with potential applications beyond antibiotic resistance, highlighting its adaptability for diverse scenarios.