High-quality data on existing bicycle infrastructure are a requirement for evidence-based bicycle network planning, which supports a green transition of human mobility. However, this requirement is rarely met: Data from governmental agencies or crowdsourced projects like OpenStreetMap often suffer from unknown, heterogeneous, or low quality. Currently available tools for road network data quality assessment often fail to account for network topology, spatial heterogeneity, and bicycle-specific data characteristics. To fill these gaps, we introduce BikeDNA, an open-source tool for reproducible quality assessment tailored to bicycle infrastructure data with a focus on network structure and connectivity. BikeDNA performs either a standalone analysis of one data set or a comparative analysis between OpenStreetMap and a reference data set, including feature matching. Data quality metrics are considered both globally for the entire study area and locally on grid cell level, thus exposing spatial variation in data quality. Interactive maps and HTML/PDF reports are generated to facilitate the visual exploration and communication of results. BikeDNA supports quality assessments of bicycle infrastructure data for a wide range of applications -- from urban planning to OpenStreetMap data improvement or network research for sustainable mobility.