Many natural phenomena can be represented by scalar fields and being able to quickly and efficiently construct an estimate of them is crucial in environmental monitoring. This study proposes an adaptive path planning algorithm for efficient scalar field reconstruction with a mobile robotic platform. By exploiting the underlying field characteristics, the path planning module focuses the sampling on informative areas that lead to a more accurate reconstruction. Sampling locations are optimized with Bayesian optimization and Gaussian process regression models the underlying field based on sampled data. Furthermore, a new acquisition function is proposed in the Bayesian optimization framework to guide the search for a more efficient solution in terms of path length and mission duration. The proposed method is compared to a commonly used exhaustive coverage path planning algorithm through numerous simulations on synthetic data and results are shown that indicate that the proposed method converges to an accurate solution significantly faster. Finally, the feasibility of real-life applications is shown in a comprehensive simulation that utilizes data collected from a natural phenomenon.