The U.S. Magnet Development Program (US-MDP) is aimed at developing high-field accelerator magnets with magnetic fields beyond the limits of Nb3Sn technology. Recent progress with composite wires and Rutherford cables based on the first generation high-temperature superconductor Bi2Sr2CaCu2O8−x (Bi2212) allows considering them for this purpose. However, Bi2212 wires and cables are sensitive to transverse stresses and strains, which are large in high-field accelerator magnets. This requires magnet designs with stress management concepts to control azimuthal and radial strains in the coil windings and prevent the degradation of the current carrying capability of Bi2212 conductor or even its permanent damage. This paper describes a novel stress management approach, which was developed at Fermilab for high-field large-aperture Nb3Sn accelerator magnets, and is now being applied to high-field dipole inserts based on Bi2212 Rutherford cables. The insert conceptual design and main parameters, including the superconducting wire and cable, as well as the coil stress management structure, key technological steps and approaches, test configurations and their target parameters, are presented and discussed.