This paper introduces a novel method to estimate distance fields from noisy point clouds using Gaussian Process (GP) regression. Distance fields, or distance functions, gained popularity for applications like point cloud registration, odometry, SLAM, path planning, shape reconstruction, etc. A distance field provides a continuous representation of the scene defined as the shortest distance from any query point and the closest surface. The key concept of the proposed method is the transformation of a GP-inferred latent scalar field into an accurate distance field by using a reverting function related to the kernel inverse. The latent field can be interpreted as a smooth occupancy map. This paper provides the theoretical derivation of the proposed method as well as a novel uncertainty proxy for the distance estimates. The improved performance compared with existing distance fields is demonstrated with simulated experiments. The level of accuracy of the proposed approach enables novel applications that rely on precise distance estimation: this work presents echolocation and mapping frameworks for ultrasonic-guided wave sensing in metallic structures. These methods leverage the proposed distance field with a physics-based measurement model accounting for the propagation of the ultrasonic waves in the material. Real-world experiments are conducted to demonstrate the soundness of these frameworks.