Text-to-SQL generation remains challenging for small and medium-sized language models, which must produce queries that are structurally valid, schema-grounded, and semantically faithful under limited inference budgets. Naive test-time scaling strategies, such as repeated sampling or unconstrained search, often spend budget on invalid, redundant, or semantically weak candidates. We present BASS, a Budget-Aware Structured Search framework for Text-to-SQL generation. BASS searches over deterministic SQL semantic units produced by rule-based Structural Boundary Detection, with lightweight admissibility filtering to reject malformed units. It scores completed candidates using an execution-gated rubric verifier: non-executable SQL receives zero reward, while executable SQL is assigned a continuous semantic score based on schema grounding, intent matching, predicate correctness, aggregation and ordering, and join/compositional structure. To improve budget usage, BASS introduces stagnation-aware branch suppression and exhaustion-aware early stopping, reallocating computation away from saturated search regions. Experiments on Spider and BIRD show strong zero-shot performance across Qwen2.5-Coder backbones. Controlled analyses further show that BASS uses fixed maximum rollout budgets adaptively, achieves better quality–cost behavior than naive repeated sampling, and benefits from semantic verification and stagnation-aware budget control.