Bismuth forms perfect atomic wires without any defects on a clean Si(001) surface. Despite the importance of this self-organized nanowire from the viewpoints of both surface science and device application, an analysis of the internal structure of the wire is quite difficult under the condition of a buried interface. In order to clarify the atomic structure of the wire capped by amorphous Si layers, the three-dimensional bismuth atomic site was measured with respect to the substrate Si lattice by the X-ray standing wave method. The results indicate that the absolute height of Bi atoms is 0.26 Å upper from the bulklike Si(004) plane of the Si-dimer layer. For the structure inside the (004) plane, Bi atoms are in the range of ±0.5 Å in the [110] direction from an intact Si-dimer position. This result disagrees with recent reports that were derived from other analytical methods used solely for a clean surface. A new model was proposed and it suggests an influence of a burying effect for the wire structure.