By generalizing the classical linear response theory of "stick" percolation to nonlinear regime, we find that the drain-current of a nanobundle thin-film transistor (NB-TFT) is described under a rather general set of conditions by a universal scaling formula ID=A/LSxi(LS/LC,rho SLS 2)timesf(VG,VD ), where A is a technology-specific constant, xi is a function of geometrical factors such as stick length LS, channel length LC, and stick density rhoS, and f is a function of drain VD and gate VG biasing conditions. This scaling formula implies that the measurement of the full current-voltage characteristics of a "single" NB-TFT is sufficient to predict the performance characteristics of any other transistor with arbitrary geometrical parameters and biasing conditions