Controllable growth of metal nanostructures on epitaxial graphene (EG) is particularly interesting and important for the applications in electric devices. Bi nanostructures on EG/SiC are fabricated through thermal decomposition of SiC and subsequent low-flux evaporation of Bi. The orientation, atomic structure, and thickness-dependent electronic states of Bi are investigated by scanning tunneling microscopy/spectroscopy. It is found that metallic Bi nanoflakes and nanorods prefer to grow on the SiC buffer layer region with higher diffusion barrier, but Bi nanoribbons are formed on regularly ordered EG. Although the thicker Bi nanoribbons of 11 monolayers on EG are still metallic, the thinner ones become semiconducting owing to the interfacial effect. This indicates that the electronic states and physical properties of Bi are substrate-dependent. The results are helpful for the design of Bi- and graphene-based electronic and spintronic devices.