To assess the current dynamics of an epidemic, it is central to collect information on the daily number of newly diseased cases. This is especially important in real-time surveillance, where the aim is to gain situational awareness, for example, if cases are currently increasing or decreasing. Reporting delays between disease onset and case reporting hamper our ability to understand the dynamics of an epidemic close to now when looking at the number of daily reported cases only. Nowcasting can be used to adjust daily case counts for occurred-but-not-yet-reported events. Here, we present a novel application of nowcasting to data on the current COVID-19 pandemic in Bavaria. It is based on a hierarchical Bayesian model that considers changes in the reporting delay distribution over time and associated with the weekday of reporting. Furthermore, we present a way to estimate the effective time-varying case reproduction number Re(t) based on predictions of the nowcast. The approaches are based on previously published work, that we considerably extended and adapted to the current task of nowcasting COVID-19 cases. We provide methodological details of the developed approach, illustrate results based on data of the current pandemic, and evaluate the model based on synthetic and retrospective data on COVID-19 in Bavaria. Results of our nowcasting are reported to the Bavarian health authority and published on a webpage on a daily basis (https://corona.stat.uni-muenchen.de/). Code and synthetic data for the analysis are available from https://github.com/FelixGuenther/nc_covid19_bavaria and can be used for adaption of our approach to different data.