We develop an M-theoretic Schwinger formalism for protected higher-derivative couplings of bulk Type IIB fields to D3-branes and derive the complete purely bosonic effective action at order $(\alpha')^2$ for bulk states scattering off the brane. Starting from the one-loop propagation of the eleven-dimensional supergravity multiplet in an M5-brane background, we reduce the corresponding vertex operators on an auxiliary two-torus and obtain a universal master formula for protected worldvolume amplitudes. Evaluating the resulting lattice sums, we derive the modular coefficient functions directly from first principles, reproducing the modular structures previously proposed for D3-brane couplings and obtaining their charged counterparts. The resulting action organises itself into sectors of definite $\mathrm{U}(1)_R$ charge, including a distinguished maximally $\mathrm{U}(1)$-violating sector, and provides a unified description of the couplings to the Type IIB bulk fields at this order.