Plasmonic bowtie nanoantennas (BNAs) can exhibit a strong enhancement of optical field, leading to large nonlinear effects. We investigated the nonlinear optical absorption of an array of BNA by femtosecond pulses, using the open-aperture Z-scan technique. The BNA array composed of paired gold nanotriangles was fabricated by nanosphere lithography. We experimentally demonstrated that upon decreasing the gap width, nonlinear absorption is enhanced due to both the enhancement of near-field coupling of nanoantennas and the minimum of the spectral detuning between the center wavelength of the laser for excitation and the localized surface plasmon resonances. The role of near-field resonant plasmonic coupling in BNA is analyzed theoretically and confirmed by our simulations.