We prove, under suitable assumptions, that p-torsion Tate–Shafarevich classes for elliptic curves over the rationals are visible in quotients of Jacobians of modular curves, as predicted by a conjecture of Jetchev–Stein. The key ingredient is the non-triviality of the Bertolini–Darmon bipartite Kolyvagin system, which implies that suitable cohomology classes of the system form a basis of the Selmer group modulo p.