Aspect-Term Sentiment Analysis (ATSA) in multi-aspect sentences faces a fundamental tradeoff between efficiency and expressiveness. Existing models either re-encode the sentence for each aspect or rely on static use of deep representations, leading to redundant computation and limited adaptivity. We argue that Transformer depth is a costly, queryable resource, and propose DABS, a single-pass inference framework that encodes each sentence once to construct a reusable, depth-ordered substrate. Each aspect then queries this shared representation to selectively read relevant tokens and abstraction levels, without re-encoding. This decouples shared sentence encoding from lightweight, aspect-conditioned readout. Experiments on four ATSA benchmarks show that DABS achieves competitive performance while reducing end-to-end computation by up to 60% in multi-aspect settings (M ≥ 2). Further analyses indicate that adaptive depth querying is most beneficial for linguistically complex cases such as negation and contrast. Code is publicly available at https://github.com/panzhzh/acl-dabs.