Improving nutrient use efficiency is an important objective in modern breeding programs. In this work, we examined potassium utilization efficiency (KUtE) and traits potentially related to it in a formerly genotyped, geographically diverse population of bread wheat (Triticum aestivum) under low potassium supply conditions. Our results unveil the existence of a large variation within the population for the traits examined. A genome-wide association study, based on a single-locus model, identified 15 markers associated with some of those traits. No marker-trait association was found using that tool for KUtE, but the use of a multi-locus approach suggested that additional marker-trait associations may be present, including whole-plant KUtE. Besides, the existence of a significant correlation between KUtE and sodium accumulation in shoots suggests the possibility of pyramiding traits associated with sodium homeostasis to improve this efficiency. In this regard, two discrete regions mapped on the long arm of chromosome 1B (1BLA and 1BLB) were associated with variation in sodium accumulation as detected with the single and multi-locus models used. Further exploration of the potential function of the genes placed in these regions, and their expression patterns, suggested likely candidates for this trait. Among the candidates placed in 1BLA region, we found TraesCS1B02G370500, TraesCS1B02G370600, and TraesCS1B02G370900, coding for putative Calcineurin B like proteins. Region 1BLB contain TraesCS1B02G388900 coding for a kinase and other genes including TraesCS1B02G389700, TraesCS1B02G389800 and TraesCS1B02G389900 coding for Ethylene-responsive transcription factors. The information here provided can be useful in breeding programs aimed to manipulate sodium accumulation through marker-assisted selection.