Sophisticated high-fidelity simulations can predict bone mass density (BMD) changes around a hip implant after implantation. However, these models currently have high computational demands, rendering them impractical for clinical settings. Model order reduction techniques offer a remedy by enabling fast evaluations. In this work, a non-intrusive reduced-order model, combining proper orthogonal decomposition with radial basis function interpolation (POD-RBF), is established to predict BMD distributions for varying implant positions. A parameterised finite element mesh is morphed using Laplace's equation, which eliminates tedious remeshing and projection of the BMD results on a common mesh in the offline stage. In the online stage, the surrogate model can predict BMD distributions for new implant positions and the results are visualised on the parameterised reference mesh. The computational time for evaluating the final BMD distribution around a new implant position is reduced from minutes to milliseconds by the surrogate model compared to the high-fidelity model. The snapshot data, the surrogate model parameters and the accuracy of the surrogate model are analysed. The presented non-intrusive surrogate model paves the way for on-the-fly evaluations in clinical practice, offering a promising tool for planning and monitoring of total hip replacements.