In this paper we analyze a system of PDEs recently introduced in [P. Amorim, Modeling ant foraging: a PDE approach with pheromones and trail formation], in order to describe the dynamics of ant foraging. The system is made of convection-diffusion-reaction equations, and the coupling is driven by chemotaxis mechanisms. We establish the wellposedness for the model, and investigate the regularity issue for a large class of integrable data. Our main focus is on the (physically relevant) two-dimensional case with boundary conditions, where we prove that the solutions remain bounded for all times. The proof involves a series of fine a priori estimates in Lebesgue spaces