Magnetic force microscopy (MFM) is a scanning microscopy technique that is commonly employed to probe the sample’s magnetostatic stray fields via their interaction with a magnetic probe tip. In this work, a quantitative, single-pass MFM technique is presented that maps one magnetic stray-field component and its spatial derivative at the same time. This technique uses a special cantilever design and a special high-aspect-ratio magnetic interaction tip that approximates a monopole-like moment. Experimental details, such as the control scheme, the sensor design, which enables simultaneous force and force gradient measurements, as well as the potential and limits of the monopole description of the tip moment are thoroughly discussed. To demonstrate the merit of this technique for studying complex magnetic samples it is applied to the examination of polycrystalline MnNiGa bulk samples. In these experiments, the focus lies on mapping and analyzing the stray-field distribution of individual bubble-like magnetization patterns in a centrosymmetric [001] MnNiGa phase. The experimental data is compared to calculated and simulated stray-field distributions of 3D magnetization textures, and, furthermore, bubble dimensions including diameters are evaluated. The results indicate that the magnetic bubbles have a significant spatial extent in depth and a buried bubble top base.