Adversarial Influence Blocking Maximization (AIBM) aims to select a set of positive seed nodes that propagate synchronously with the known negative seed nodes to counteract their negative influence. Time factor plays a particularly vital role for many AIBM application scenarios. However, the AIBM problem with time constraint remains unexplored. More importantly, existing AIBM studies have not thoroughly investigated the submodularity of the objective function, thereby failing to establish a theoretical approximation guarantee. To address these challenges, firstly, we establish the Time-Critical Adversarial Influence Blocking Maximization (TC-AIBM), which explicitly incorporates time constraint. Then, we provide a theoretical proof of the submodularity of the TC-AIBM objective function under three different tie-breaking rules. Finally, a Bidirectional Influence Sampling (BIS) algorithm is proposed to solve the TC-AIBM problem. Leveraging the monotonicity and submodularity of the objective function, BIS achieves an approximation guarantee of $(1-1/e-ε)(1-ψ)$. Comprehensive experiments on four real-world datasets demonstrate that the proposed BIS algorithm exhibits excellent robustness across various negative seeds, time constraint, and tie-breaking rules, outperforming state-of-the-art baselines. In addition, BIS is up to three orders of magnitude faster than the Greedy algorithm.