Generally, EEG potentials are primarily averaged over trials, not electrodes. Averaging over electrodes is often done in addition to trial averaging, but this by itself does not make the potentials visible on a single-trial basis since the "noise" overshadowing the potentials is largely shared by all adjacent electrodes.
The Bereitschaftspotential is also averaged over trials, especially since it is usually specified to be observed over specific electrodes.
As you note in a comment, single-trial identification of EEG phenomena, such as the Bereitschaftspotential (or the P300), is being attempted using machine learning techniques. However, these work far from reliably, and the original work on the Bereitschaftspotential was done far before these powerful machine learning techniques became available. So in the original BP work, averaging was done over trials (and often, over subjects, too). This is apparent in for example the Methods section of Libet's famous paper from 1983 (p. 624):
For present purposes, analysis of RPs is made for those recorded at the vertex, where they were all maximal. ... 40 trials were performed and averaged by a computer of average transients
The vertex = electrode Cz.