Electrical characterizations on webs of highly ordered semiconducting polymer nanofibers (NFs) are often performed with large electrodes devices (millimeter scale) for which the carrier transport is an average between transport within isolated NFs and transport at the intersection of two or more NFs. In order to assess the nanoscale electrical properties of the NFs, a field-effect transistor based on conductive atomic force microscopy is introduced that allows the visualization of the current distribution at the nanometer scale within a web of poly(3-butylthiophene) NFs. The contact resistance is evaluated to be ≈4 kΩ cm, which does not limit the charge transport process, and the mobility in one single NF is μNF = 0.07 ± 0.03 cm2 V−1 s−1. One NF can carry a current density of 20 kA cm−2 without being destroyed. Moreover, by observing the current maps in detail, it is found that the electrical resistance associated with the bridging of two or more individual NFs does not reduce the charge transport inside the web of NFs. Finally, different kinds of bridging geometries are shown and the role of tie molecules is discussed.