The organic terahertz (THz) generation crystal BNA has recently gained traction as a source for producing broadband THz pulses. When pumped with 100 fs pulses, the thin BNA crystals can produce relatively high electric fields with frequency components out to 5 THz. However, the THz output with 800-nm pump wavelength is limited by the damage threshold of the material, particularly when using a 1 kHz or higher repetition rate laser. Here, we report that the damage threshold of BNA THz generation crystals can be significantly improved by bonding BNA to a high-thermal conductivity sapphire window. When pumped with 800-nm light from an amplified Ti:sapphire laser system, this higher damage threshold enables generation of 2.5× higher electric field strengths compared to bare BNA crystals. We characterize the average damage threshold for bare BNA and BNA-sapphire, measure peak-to-peak electric field strengths and THz waveforms, and determine the nonlinear transmission in BNA. Pumping BNA bonded to sapphire with 3 mJ 800-nm pulses results in peak-to-peak electric fields exceeding 1 MV/cm, with broadband frequency components >3 THz. This high-field, broadband THz source is a promising alternative to tilted pulse front LiNbO3 THz sources, enabling many research groups without optical parametric amplifiers to perform high-field, broadband THz spectroscopy.