The article addresses the problem of dynamic system identification in the errors-in-variables framework for a class of discrete-time time-invariant input-output bilinear models when subjected to a white input signal. The proposed algorithm is based on an extension of the bias-compensated least squares method and utilises the Frisch scheme equations to determine the parameter vector together with the variances of the input and output noise sequences. The appropriateness of the approach is analysed and its performance evaluated when compared to other errors-in-variables identification techniques by means of a Monte Carlo simulation. The results obtained demonstrate the accuracy of the proposed method and the performance in terms of noise robustness is also observed.