The development of fast detection methods for comprehensive monitoring of electron bunches is a prerequisite to gain comprehensive control over the synchrontron emission in storage rings with their MHz repetition rate. Here, we present a proof-of-principle experiment with at detailed description of our implementation to detect the longitudinal electron bunch profiles via single-shot, near-field electro-optical sampling at the Karlsruhe Research Accelerator (KARA). Our experiment is equipped with an ultra-fast line array camera providing a high-throughput MHz data stream. We characterize statistical properties of the obtained data set and give a detailed description for the data processing as well as for the calculation of the charge density profiles, which where measured in the short-bunch operation mode of KARA. Finally, we discuss properties of the bunch profile dynamics on a coarse-grained level on the example of the well-known synchrotron oscillation.