The remediation of bromate in water is a concern due to the reported health issues caused by its ingestion. Catalytic processes, wherein bromate is reduced to non-hazardous bromide, have been studied. In the present work, catalysts of 1% palladium supported in electrospun carbon fibers (Pd-CFs) using different methods for palladium incorporation were prepared. The textural properties, morphology, crystalline structure, and hydrogenation capacity by H2 chemisorption analysis of the Pd-CFs catalysts were characterized. The catalytic tests were performed in a semi-batch reactor, and the obtained results showed different catalytic activity by each prepared Pd-CFs catalyst. The catalysts prepared by incipient wetness impregnation—1% Pd/CF1 and 1% Pd/CF2, using CFs obtained with electrospinning flow rates of 0.5 mL h−1 and 2 mL h−1, respectively—achieved total bromate reduction after 120 min of operation; however, 1% Pd/CF1 obtained total reduction as early as 30 min. Taking into account the catalyst properties, 1% Pd/CF1 showed a good catalytic activity due to CFs morphology obtained using a low electrospinning flow rate, while the Pd incorporation method allowed a high availability of active sites with hydrogenation properties for bromate reduction.