The bremsstrahlung x-ray emission profile from high intensity laser-solid interactions provides valuable insight to the internal fast electron transport. Using penumbral imaging, we characterise the spatial profile of this bremsstrahlung source as a function of laser intensity by incrementally increasing the laser focal spot size on target. The experimental data shows a dual-source structure; one from the central channel of electrons, the second a larger substrate source from the recirculating electron current. The results demonstrate than an order of magnitude improvement in the intensity contrast between the two x-ray sources is achieved with a large focal spot, indicating preferable conditions for applications in radiography. An analytical model is derived to describe the transport of suprathermal electron populations that contribute to substrate and central channel sources through a target. The model is in good agreement with the experimental results presented here and furthermore is applied to predict laser intensities for achieving optimum spatial contrast for a variety of target materials and thicknesses.