Ingredients used to enhance sensory quality of gluten-free (GF) bread often lack in nutrients. This presents nutritional challenges for celiac-positive individuals and fails to meet expectations of healthfulness for non-celiac GF consumers. Sorghum (Sorghum bicolor L. Moench) flour can provide acceptable GF bread properties, and tannin-containing varieties contain antioxidants concentrated in the bran along with dietary fiber. Using a central composite design, tannin-containing sumac sorghum bran, gum (xanthan + guar), and water levels were optimized in a GF sorghum-based bread formulation. Loaf specific volume and gas cells/cm2 were maximized while minimizing hardness and cell wall thickness. The optimum formulation containing 14.2% sorghum bran, 1% gum, and 145% water (flour basis) effectively increased dietary fiber in bread to 13.4% (considered "high fiber") and showed oxygen radical absorbance capacity of 61.6 µmol TE/g. This optimum formulation did not differ from a sorghum flour-based control bread in consumers' (N = 100) liking of color, texture, flavor, overall acceptability, nor willingness to buy (WTB). All mean hedonic scores (numbered 9-point scale) were above 5, whereas average WTB was 4.7 for the optimum formulation and 4.6 for the control (9-point Likert scale) among consumers varying in GF bread consumption habits. Perceived bread bitterness was low (averaging 2.85 on 9-point intensity scale), did not vary between samples despite marked differences in antioxidant capacity, and was not correlated with WTB. When utilizing effective optimization models with key functional ingredients, sumac sorghum bran addition can enhance dietary fiber and antioxidant potential in sorghum-based GF breads without compromising quality attributes.