The ultrafast optoelectronic response in topological insulators (TIs) has been recognized as one of the keys for applications on quantum computing and high-speed devices, which thus has attracted great attention recently. In this work, we systematically investigate the ultrafast transient terahertz emission excited by femtosecond laser pulses in Bi2Te3 with terahertz emission spectroscopy serving as an ultrafast and contactless detector. The nonlinear terahertz emission surpasses the terahertz emission from the sum of the drift and diffusion current contributions even at oblique incidence with an incident angle up to 70°, manifesting remarkable surface nonlinear effects on TIs. Quantitatively comprehensive microscopic analysis of the nonlinear terahertz emission origins indicates the 120°-periodic azimuth-angle dependence, which reveals a microscopic picture that the nonlinear current flows along the Bi-Te bonds. Our exploration not only enhances the microscopic understanding of the nonlinear responses in TIs on a femtosecond timescale but also lays a foundation for their applications on high-speed and low-power-consumption devices and systems.