The mechanisms and kinetics of the biopolymer changes linked to bean softening during cooking at 95 °C were explored in bean accessions with different cooking behaviour. The cotyledons of non-aged (fresh) and aged beans of five slow to fast cooking bean accessions were split for texture-based classification. Individual half cotyledons were classified into narrow texture ranges and their corresponding half cotyledons from the three main texture classes were assessed for detailed texture evolution, starch gelatinization, protein denaturation, and pectin solubilization during cooking. The cooking behaviour of the half (split) beans varied across accessions and storage conditions, with delayed softening in aged half beans. For an accession, split fresh beans had faster softening compared to their corresponding whole fresh beans, while split and whole aged beans had comparable softening rate. For both fresh and aged half beans of all accessions, residual starch gelatinization and protein denaturation were completed within 5–10 min and 20–30 min, respectively, which times are far in advance of the plateau texture that was attained after 30–40 min and 180–240 min of cooking for fresh and aged beans, respectively. No link between the protein denaturation and starch gelatinization rates and that of softening was observed. The extent of pectin solubilization for the different bean accessions, fresh and aged, reached a plateau at the same time as texture. During cooking, the extent and rate constant of pectin solubilization significantly align with respectively texture decay (negatively, r = 0.87–0.99, p ≤ 0.0002) and the softening rate constant (positively, r = 0.98, p < 0.0001). Thus, softening during cooking of beans of different accessions, fresh or aged, is largely directly influenced by pectin solubilization with protein denaturation playing less influence and starch gelatinization having little to no influence.