This paper explores the potential of a learned two-layer B-frame codec, known as TLZMC. TLZMC is one of the few early attempts that deviate from the hybrid-based coding architecture by skipping motion coding. With TLZMC, a low-resolution base layer is utilized to encode temporally unpredictable information. We address the question of whether adapting the base-layer bitrate can achieve better rate-distortion performance. We apply the feature map modulation technique to enable per-frame bitrate adaptation of the base layer. We then propose and compare three online search strategies for determining the base-layer rate parameter: per-level brute-force search, per-level greedy search, and per-frame greedy search. Experimental results show that our top-performing search strategy achieves 0.6%-15.8% Bjøntegaard-Delta rate savings over TLZMC.