Swarm robotic search aims at searching targets using a large number of collaborating simple mobile robots, with applications to search and rescue and hazard localization. In this regard, decentralized swarm systems are touted for their coverage scalability, time efficiency and fault tolerance. To guide the behavior of such swarm systems, two broad classes of approaches are available, namely nature-inspired swarm heuristics and multi-robotic search methods. However, the ability to simultaneously achieve efficient scalability and provide fundamental insights into the exhibited behavior (as opposed to exhibiting a black-box behavior), remains an open problem. To address this problem, this paper extends the underlying search approach in batch-Bayesian Optimization to perform search with embodied swarm agents operating in a (simulated) physical 2D arena. Key contributions lie in: 1) designing an acquisition function that not only balances exploration and exploitation across the swarm, but also allows modeling knowledge extraction over trajectories; and 2) developing its distributed implementation to allow asynchronous task inference and path planning by the swarm robots. The resulting collective informative path planning approach is tested on target-search case studies of varying complexity, where the target produces a spatially varying (measurable) signal. Notably superior performance, in terms of mission completion efficiency, is observed compared to exhaustive search and random walk baselines as well as a swarm optimization-based state-of-the-art method. Favorable scalability characteristics are also demonstrated.