We introduce mildly Hurewicz property in the setting of bitopological spaces and study this concept along with that of almost Hurewicz property introduced by A. E. Eysen and S. Özcağ in [4]. Some connections between these properties and Hurewicz property are highlighted. We investigate the preservation of almost Hurewicz property and of mildly Hurewicz property under various types of mappings between bitopological spaces.