Organizations are increasingly exploring delegation of screening and negotiation tasks to AI systems, yet deployment in high-stakes B2B settings is constrained by governance: preventing unauthorized commitments, ensuring sufficient information before bargaining, and maintaining effective human oversight and auditability. Prior work on large language model negotiation largely emphasizes autonomous bargaining between agents and omits practical needs such as staged information gathering, explicit authorization boundaries, and systematic feedback integration. We propose GAIA, a governance-first framework for LLM-human agency in B2B negotiation and screening. GAIA defines three essential roles - Principal (human), Delegate (LLM agent), and Counterparty - with an optional Critic to enhance performance, and organizes interactions through three mechanisms: information-gated progression that separates screening from negotiation; dual feedback integration that combines AI critique with lightweight human corrections; and authorization boundaries with explicit escalation paths. Our contributions are fourfold: (1) a formal governance framework with three coordinated mechanisms and four safety invariants for delegation with bounded authorization; (2) information-gated progression via task-completeness tracking (TCI) and explicit state transitions that separate screening from commitment; (3) dual feedback integration that blends Critic suggestions with human oversight through parallel learning channels; and (4) a hybrid validation blueprint that combines automated protocol metrics with human judgment of outcomes and safety. By bridging theory and practice, GAIA offers a reproducible specification for safe, efficient, and accountable AI delegation that can be instantiated across procurement, real estate, and staffing workflows.