An observer for a bilinear system with an unknown unmeasurable disturbance is considered. Necessary and sufficient conditions for the existence of disturbance decoupled full order and minimal order observers are formulated. The conditions analogous to detectability and pole assignment of linear observers are also given. These conditions provide a basis for verification of observer existence and design procedures to select observer matrices using straightforward matrix calculus. The observers are intended for application to the state estimation of a semi-active vehicle suspension system and the design procedures are illustrated for this particular case. The procedures developed, however, are general and can be applied to any bilinear system.