Despite the rapid and dynamic evolution of research into dietary polyphenols, there is still a knowledge gap regarding their bioaccessibility since it could be influenced by the chemical and nutritional compositions of the food matrix. This study aimed to describe the impact of food thickeners (xanthan gum, guar gum, β-glucan, pectin) on the bioactivity of flavonoids from saffron floral by-products in model beverages before and after thermal processing. The different beverage formulas were characterized in terms of polyphenolic composition using HPLC-DAD-ESI-MSn and rheological properties. The impact of food thickeners and thermal processing on the inhibition of digestive enzymes was also determined. The model beverages mainly presented glycosylated flavonols (of kaempferol, quercetin, and isorhamnetin), with a reduced content in some heat-treated samples. The inhibitory effect on α-amylase was only detected in heat-treated beverages, showing the formulation without any thickener to have the greatest inhibitory effect. Finally, the presence of saffron floral by-products in the beverages showed a tendency to decrease the flow consistency index (K) and an increase in the flow behavior index (n), most probably driven by the aggregation of phenolics with thickeners. Therefore, this research provides new insights into the development of flavonoid-rich beverages in order to ensure that they exert the expected beneficial effects after their ingestion.