Fe(1+y)Te with y≲0.05 exhibits a first-order phase transition on cooling to a state with a lowered structural symmetry, bicollinear antiferromagnetic order, and metallic conductivity, dρ/dT>0. Here, we study samples with y=0.09(1), where the frustration effects of the interstitial Fe decouple different orders, leading to a sequence of transitions. While the lattice distortion is closely followed by incommensurate magnetic order, the development of bicollinear order and metallic electronic coherence is uniquely associated with a separate hysteretic first-order transition, at a markedly lower temperature, to a phase with dramatically enhanced bond-order wave (BOW) order. The BOW state suggests ferro-orbital ordering, where electronic delocalization in ferromagnetic zigzag chains decreases local spin and results in metallic transport.