Soft red winter wheat (SRW) is characterized by high yield and relatively low protein content. In Kentucky, there is growing demand from local artisan bread bakers for regionally produced flour, requiring production of grain with increased protein content and/or strength. The objective of this two-year field experiment was to evaluate the effect of nitrogen (N) management on five cultivars of winter wheat on yield and bread baking quality traits of modern and landrace SRW cultivars (Triticum aestivum L.). All five cultivars were evaluated using two N application rates in conventional and organic production systems. All traits measured were significantly affected by the agricultural production system and N rate, although plant height and other quality traits varied by study year. Significantly higher yields were achieved in the conventional system at a relatively low N rate (67.2 kg ha−1) in both study years (2017–2019) (p < 0.01). Results were variable by cultivar and a locally bred, high-yielding cultivar (Pembroke 2014) had the highest lactic acid solvent retention capacity score and thousand kernel weight of the cultivars evaluated. In addition, a landrace cultivar (Purple Straw) had the highest grain N and plant height. A French soft wheat, Soissons, had the highest sedimentation value and Pembroke 2016 achieved the highest yield. The findings from this study suggest the possibility of attaining a desirable grain with quality traits of SRW wheat that meets the needs of local bread wheat production in Kentucky through improving the optimization of cultivar selection, N management and specific considerations for conventional and organic systems.