In many applications, a state-space model depends on a parameter which needs to be inferred from data in an online manner. In the maximum likelihood approach, this can be achieved using stochastic gradient search, where the underlying gradient estimation is based on the optimal filter and the optimal filter derivative. However, the optimal filter and its derivative are not analytically tractable for a nonlinear state-space model and need to be approximated numerically. In [G. Poyiadjis, A. Doucet, and S. S. Singh, Biometrika, 98 (2011), pp. 65-80], a particle approximation to this derivative has been proposed, while the corresponding central limit theorem and L-p error bounds have been established in [P. Del Moral, A. Doucet, and S. S. Singh, SIAM T. Control Optim., 53 (2015), pp. 1278-1304]. We derive here bounds on the bias of this particle approximation. Under mixing conditions, these bounds are uniform in time and inversely proportional to the number of particles.