A single-field bilinear system generating the so-called non-local Boussinesq equation is constructed. From the bilinearization procedure it can be seen that the associated hierarchy of soliton systems which we construct shares part of the solution set of a hierarchy related to the Kadomtsev-Petviashvili equation. A bilinear representation of the recursion operator for the Kaup hierarchy is essential in the construction and a systematic way of obtaining such a representation from just two-soliton considerations is presented.