In this paper, we illustrate the synthesis, characterization, and application of a Bovine Serum Albumin-stabilized copper nanocluster (BSA@CuNCs)-based photoluminescence (PL) bifunctional sensor for the selective and rapid sensing of picric acid (PA) and hydrogen peroxide (H2O2). Blue-emitting copper nanoclusters were synthesized using one-pot synthesis at room temperature. The PL intensity of BSA@CuNCs was shown to be quenched (“Turn-off”) with an increase in the concentration of PA and intensified (“Turn-on”) with the addition of H2O2. The quenching of PL intensity of BSA@CuNCs was shown to be extremely selective and rapid towards PA. A linear decrease in the PL emission intensity of BSA@CuNCs was observed with a PA concentration in the range of 0–15 μM. An extremely low detection limit of 60 nM (3σ/k) was calculated. The as-prepared BSA@CuNCs also exhibited superior selectivity for PA detection in aqueous medium. The developed sensor was also utilized for the sensing of PA in natural water samples. The probe was found to be extremely sensitive towards the detection of H2O2. An increase in the PL intensity of BSA@CuNCs was seen with the addition of H2O2, with a detection limit of 0.11 μM.