The need for accurate physical measurements is omnipresent in both scientific and engineering applications. Such measurements can be used to explore and characterize the behavior of a system over the parameters of interest. These procedures are often very costly and time-consuming, requiring many measurements or samples. Therefore, a suitable data collection strategy can be used to reduce the cost of acquiring the required samples. One important consideration which often surfaces in physical experiments, like near-field measurements for electromagnetic compliance testing, is the total path length between consecutively visited samples by the measurement probe, as the time needed to travel along this path is often a limiting factor. A line-based sampling strategy optimizes the sample locations in order to reduce the overall path length while achieving the intended goal. Previous research on line-based sampling techniques solely focused on exploring the measurement space. None of these techniques considered the actual measurements themselves despite these values hold the potential to identify interesting regions in the parameter space, such as an optimum, quickly during the sampling process. In this paper, we extend Bayesian optimization, a point-based optimization technique into a line-based setting. The proposed algorithm is assessed using an artificial example and an electromagnetic compatibility use-case. The results show that our line-based technique is able to find the optimum using a significantly shorter total path length compared to the point-based approach.