Radial electric field bifurcation induced by electrode biasing near the tokamak edge is considered in this paper. The radial electric field structure is analysed including two non-linear terms in the radial current, namely the neoclassical term and the orbit loss term. Their competition gives various radial electric field structures, and biasing transition is compared with spontaneous transition. Bifurcation has different features for positive and negative biasing, with a larger number of structures available for the negative biasing case. Effectiveness of the solitary radial electric field structures induced by biasing for confinement improvement is discussed.