Near-term quantum devices provide only finite-shot computational-basis measurement outcomes and typically prepare imperfect, contaminated states rather than exact ground states. This practical constraint motivates algorithms that can convert samples into reliable estimates of low-energy properties without full state tomography or exhaustive Hamiltonian measurement. In this work we propose Active Sampling Sample-based Quantum Diagonalization (AS-SQD), an approach that frames Sample-based Quantum Diagonalization (SQD) as an active learning problem: given a finite multiset of measured bitstrings, which additional basis states should be included in the effective subspace to most efficiently recover the true ground-state energy? SQD constructs an effective low-dimensional eigenvalue problem by restricting the Hamiltonian to the span of a selected set of computational basis states and then classically diagonalizing the restricted matrix. However, naive SQD that only uses the sampled subspace often suffers from severe bias under finite-shot sampling and excited-state contamination, while blind subspace expansion (e.g., random exploration of connected basis states) is inefficient and unstable as system size grows. We introduce a perturbation-theoretic acquisition function based on Epstein-Nesbet second-order energy corrections to rank candidate basis states that are connected to the current subspace by the Hamiltonian. At each iteration, AS-SQD (i) diagonalizes the restricted Hamiltonian to obtain an approximate ground state, (ii) generates a candidate set of connected basis states, and (iii) adds the most valuable candidates according to a scoring function derived from perturbation theory. We evaluate AS-SQD on disordered Heisenberg and Transverse-Field Ising (TFIM) spin chains up to 16 qubits under a realistic preparation model that mixes 80% ground state and 20% first excited state. Furthermore, we validate the inherent robustness of our approach against real-world state preparation and measurement (SPAM) errors using physical samples directly from an IBM Quantum processor. Across both simulated and physical evaluations, AS-SQD consistently reduces energy errors by orders of magnitude compared with standard SQD and random expansion. Detailed ablation studies isolate the driving mechanisms of the perturbation score, demonstrating that physics-guided basis acquisition effectively concentrates computation on energetically relevant directions and bypasses exponential combinatorial bottlenecks.