Turbulent states are ubiquitous in plasmas, and the understanding of turbulence is fundamental in modern astrophysics. Numerical simulations, which are the state-of-the-art approach to the study of turbulence, require substantial computing resources. Recently, attention shifted to methods for generating synthetic turbulent magnetic fields, affordably creating fields with parameter-controlled characteristic features of turbulence. In this context, the BxC toolkit was developed and validated against direct numerical simulations (DNSs) of isotropic turbulent magnetic fields. Here, we demonstrate novel extensions of BxC to generate realistic turbulent magnetic fields in a fast, controlled, geometric approach. First, we perform a parameter study to determine quantitative relations between the BxC input parameters and the desired characteristic features of the turbulent power spectrum, such as the extent of the inertial range, its spectral slope, and the injection and dissipation scale. Second, we introduce in the model a set of structured background magnetic fields, B0, as a natural and more realistic extension to the purely isotropic turbulent fields. Third, we extend the model to include anisotropic turbulence properties in the generated fields. With all these extensions combined, our tool can quickly generate any desired structured magnetic field with controlled, anisotropic turbulent fluctuations, faster by orders of magnitude with respect to DNSs. These can be used, e.g., to provide initial conditions for DNSs or easily generate synthetic data for many astrophysical settings, all at otherwise unaffordable resolutions.