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Recently, hybrid band communications have received much attention to fulfil the exponentially growing user demands in next-generation communication networks. Still, determining the best band to communicate over is a challenging issue, especially in the dynamic channel conditions in multi-band wireless systems. In this paper, we manipulate a practical online-learning-based solution for the best band/channel selection in hybrid radio frequency and visible light communication (RF/VLC) wireless systems. The best band selection difficulty is formulated as a multi-armed bandit (MAB) with cost subsidy, in which the learner (transmitter) endeavors not only to increase his total reward (throughput) but also reduce his cost (energy consumption). Consequently, we propose two hybrid band selection (HBS) algorithms, named cost subsidy upper confidence bound (CSUCB-HBS) and cost subsidy Thompson sampling (CSTS-HBS), to efficiently handle this problem and obtain the best band with high throughput and low energy consumption. Extensive simulations confirm that CSTS-/CSUCB-HBS outperform the naive TS/UCB and heuristic HBS approaches regarding energy consumption, energy efficiency, throughput, and convergence speed.