Extrusion bioprinting based on the development of novel bioinks offers the possibility of manufacturing clinically useful tools for wound management. In this study, we show the rheological properties and printability outcomes of two advanced dressings based on platelet-rich plasma (PRP) and platelet-poor plasma (PPP) blended with alginate and loaded with dermal fibroblasts. Measurements taken at 1 h, 4 days, and 18 days showed that both the PRP- and PPP-based dressings retain plasma and platelet proteins, which led to the upregulation of angiogenic and immunomodulatory proteins by embedded fibroblasts (e.g., an up to 69-fold increase in vascular endothelial growth factor (VEGF), an up to 188-fold increase in monocyte chemotactic protein 1 (MCP-1), and an up to 456-fold increase in hepatocyte growth factor (HGF) 18 days after printing). Conditioned media harvested from both PRP and PPP constructs stimulated the proliferation of human umbilical vein endothelial cells (HUVECs), whereas only those from PRP dressings stimulated HUVEC migration, which correlated with the VEGF/MCP-1 and VEGF/HGF ratios. Similarly, the advanced dressings increased the level of interleukin-8 and led to a four-fold change in the level of extracellular matrix protein 1. These findings suggest that careful selection of plasma formulations to fabricate wound dressings can enable regulation of the molecular composition of the microenvironment, as well as paracrine interactions, thereby improving the clinical potential of dressings and providing the possibility to tailor each composition to specific wound types and healing stages.