Horizontal pressure gradient fluctuations caused by a bubble passage in the neighbourhood of the probe are simulated using Davidson's pressure field around a circular bubble. The salient features of these fluctuations are studied with regard to their sensitivity to the obliquity and randomness of the bubble traversing path. The utility aspects of horizontal pressure differential measurements over vertical pressure differentials are highlighted and a qualitative comparison between the simulated and those experimentally obtained from a two-dimensional bed, showing strong similarities are presented.