The burden of respiratory illnesses is large, having a significant impact on healthcare systems worldwide. As researchers work to better understand chronic diseases as well as newly emerging respiratory viruses, the need for improved respiratory models has become evident. While three-dimensional (3D) bioprinting has been illustrated as a feasible method to create complex cellularized constructs or respiratory models, it has yet to be determined whether including relevant biomechanical stimulus and/or including relevant growth factors has a significant impact on the response of respiratory tissue models to infection. In this study, an alginate/gelatin/collagen solution was synthesized and characterized in terms of rheology, printability, degradation, mechanical properties, and biocompatibility. The bioink which incorporated primary human pulmonary fibroblasts and THP-1 cells was bioprinted to form hierarchical 3D constructs, which were then seeded with primary human bronchial epithelial cells to form the respiratory tissue model. To explore the importance of growth factors and culture conditions in modelling infection, we strategically developed a hepatocyte-growth-factor-loaded nanoparticle system and incorporated them into the bioink for bioprinting the respiratory tissue model and then cultured the model under dynamic conditions in a breath-mimicking bioreactor. The effect of including growth factors and dynamic culture conditions was examined over a 28-day period, followed by the infection of these constructs with influenza A virus. It was determined that these constructs support infection, demonstrating a more clinically relevant infection pattern than 2D models. It was further determined that inclusion of hepatocyte growth factor aids in epithelial cell growth, while inclusion of biomechanical stimulus increases cellular metabolism and has a moderating effect on response to infection.