In mission-based mobile environments such as airplane maintenance, workflow-based mobile sensor networks emerge, where mobile users (MUs) with sensing devices visit sequences of mission-driven locations defined by workflows, and demand the gathering of sensory data within mission durations. To satisfy this demand in a cost-efficient manner, mobile access point (AP) deployment needs to be part of the overall solution. Therefore, we study the mobile AP deployment in workflow-based mobile sensor networks. We categorize MUs' workflows according to a priori knowledge of MUs' staying durations at mission locations into complete and incomplete information workflows. In both categories, we formulate the cost-minimizing mobile AP deployment problem into multiple (mixed) integer optimization problems, satisfying MUs' QoS constraints. We prove that the formulated optimization problems are NP-hard and design approximation algorithms with guaranteed approximation ratios. We demonstrate using simulations that the AP deployment cost calculated using our algorithms is 50-60% less than the stationary baseline approach and fairly close to the optimal AP deployment cost. In addition, the run times of our approximation algorithms are only 10-25% of those of the branch-and-bound algorithm used to derive the optimal AP deployment cost.