This paper extends the discussion about the bus network design in face of the mobility patterns associated with different degrees of urban dispersion. Based on an analytical approach, a comparison of total costs among different network structures is made for a ring-radial city, which is the other most common regular city layout. The results clarify what structure is the best solution for different scenarios of dispersion and city and transport characteristics. Simultaneously, the effect of the street pattern on the applicability of each structure is evaluated comparing these results to a previous research for a grid city. Three basic structures are analyzed: a radial scheme, a direct-trip-based network, and a hybrid structure as a transfer-based alternative. Each structure is dominant for a specific range of dispersion: radial networks for scenarios of high concentration, direct-trip-based systems for intermediate degrees of dispersion, and transfer-based structures when the activities are decentralized. However, constraints on stop capacity modify these ranges. Each structure presents a different distribution of travel time in the transit chain and agency costs that determine the most competitive alternative. In addition, the behavior of the structures and the evolution of costs regarding urban decentralization are practically the same for both street patterns: system costs grow with increasing mobility dispersion, the range of applicability for each structure is the same, and changes in their applicability when main input parameters vary are very similar. Therefore, these results make it possible to generalize about the conclusions obtained independently of the street layout.