This paper investigates H_∞ reduced order unbiased filtering problems for a nominal bilinear system and a bilinear system affected by norm-bounded structured uncertainties in all the system matrices. First, the unbiasedness condition is derived. Second, a change of variable is introduced on the inputs of the system to reduce the conservatism inherent to the filter stability requirement and to treat the product of the inputs by the disturbances. Then the solution is expressed in terms of LMI by transforming the problem into a robust state feedback in the nominal case and a robust static output feedback in the uncertain case.