The electron-phonon coupling strength in single-wall carbon nanotube (SWNT) bundles has been studied directly in the time-domain by femtosecond time-resolved photoelectron spectroscopy. We have measured the dependence of H(Te,Tl), the rate of energy-transfer between the electronic system and the lattice as a function of electron and lattice temperatures Te and Tl . The experiments show that H scales approximately with the 5th power of the electron- and lattice-temperatures. The results can be related to the e-ph mass enhancement parameter l. The experimentally obtained value for l/Q2, where Q is the Debye temperature, suggests that e-ph scattering times at the Fermi level of SWNT bundles can be exceptionally long, exceeding 1.5 ps at room temperature.