We describe a technique for characterizing bolometric detectors that have sufficient sensitivity to count single terahertz photons. The device is isolated from infrared blackbody radiation and a single terahertz photon is simulated by a fast microwave pulse, where the absorbed energy of the pulse is equal to the photon energy. We have employed this technique to characterize bolometric detectors consisting of a superconducting titanium nanobridge with niobium contacts. Present devices have Tc, = 0.3 K and a measured intrinsic energy resolution of approximately 6 terahertz fullwidth at half-maximum, near the predicted value due to intrinsic thermal fluctuation noise, with a time constant of 2μis. An intrinsic energy resolution of 1 terahertz should be achievable by reducing the volume of the titanium nanobridge. Such a detector has important applications in future space-based terahertz astronomy missions.