High-cadence, multiwavelength observations and simulations are employed for the analysis of solar photospheric magnetic bright points (MBPs) in the quiet Sun. The observations were obtained with the Rapid Oscillations in the Solar Atmosphere (ROSA) imager and the Interferometric Bidimensional Spectrometer at the Dunn Solar Telescope. Our analysis reveals that photospheric MBPs have an average transverse velocity of approximately 1 km s−1, whereas their chromospheric counterparts have a slightly higher average velocity of 1.4 km s−1. Additionally, chromospheric MBPs were found to be around 63 per cent larger than the equivalent photospheric MBPs. These velocity values were compared with the output of numerical simulations generated using the MURAM code. The simulated results were similar, but slightly elevated, when compared to the observed data. An average velocity of 1.3 km s−1 was found in the simulated G-band images and an average of 1.8 km s−1 seen in the velocity domain at a height of 500 km above the continuum formation layer. Delays in the change of velocities were also analysed. Average delays of ∼4 s between layers of the simulated data set were established and values of ∼29 s observed between G-band and Ca II K ROSA observations. The delays in the simulations are likely to be the result of oblique granular shock waves, whereas those found in the observations are possibly the result of a semi-rigid flux tube.