The radio signature of a shock travelling through the solar corona is known as a type II solar radio burst. In rare cases, these bursts can exhibit a fine structure known as ‘herringbones’ which are a direct indicator of particle acceleration occurring at the shock front. However, few studies have been performed on herringbones and the details of the underlying particle acceleration processes are unknown. Here, we use an image processing technique known as the Hough transform to statistically analyse the herringbone fine structure in a radio burst at 20–90MHz observed from the Rosse Solar–Terrestrial Observatory on 2011 September 22. We identify 188 individual bursts which are signatures of bi-directional electron beams continuously accelerated to speeds of 0.16 c. This occurs at a shock acceleration site initially at a constant altitude of 0.6 R in the corona, followed by a shift to 0.5 R. The anti-sunward beams travel a distance of 170 Mm (and possibly further) away from the acceleration site, while those travelling toward the sun come to a stop sooner, reaching a smaller distance of 112 Mm. We show that the stopping distance for the sunward beams may depend on the total number density and the velocity of the beam. Our study concludes that a detailed statistical analysis of herringbone fine structure can provide information on the physical properties of the corona which lead to these relatively rare radio bursts.