Consumers’ recognition and understanding of food characteristics can have an important role when making purchase decisions. The current study analysed consumer preferences for bread, an important food in the diets of Central European countries. The study included a conjoint experiment on a representative sample of 547 adult consumers in Slovenia. The following bread attributes: functional ingredients (chia seeds, linseed, quinoa, and Tartary buckwheat); nutritional claims (low salt, high fibre, and high protein); and other claims (organic, free from additives, flour from Slovenia, and wholegrain) were studied. The results showed the strongest relative importance for functional ingredients (a mean relative importance of 83.9%). In addition, a deeper insight into consumer preference was investigated by a recently developed modular instrument for food-related lifestyles. Latent class cluster analysis (LCA) enabled the identification of four consumer segments (uninvolved, conservative, health-conscious, and moderate) with different preferences toward selected functional ingredients, nutrition, and other claims. The results provide insights that allow for a better understanding of consumer preferences for functional ingredients and claims, and new perspectives for bread marketing to different consumer segments based on food-related lifestyles. Identifying the drivers that affect bread purchasing and consumption can support reformulation activities and product promotion in the direction of reinforcing healthier food choices.