•Formulated parsimonious, continuous model for optimizing the design of hybrid transit networks fed by shared bikes.•Significant cost savings were found in some cases over transit networks accessed on foot only and those accessed by feeder buses.•Jointly optimized transit and shared-bike systems can reduce costs for both patrons and the transit agency.•Revenue accrued from system-optimal pricing for shared bikes can often cover their cost, with or without subsidy. Transit systems are designed in which access and egress can occur via a shared-bike service. Patrons may walk to shared-bike docking stations nearest their origins, and then cycle to their nearest transit stations where they deposit the bikes. The travel pattern is reversed when patrons cycle from their final transit stations on to their destinations. Patrons choose between this option and that of solely walking to or from transit stations. Shared bikes are priced to achieve the system-optimal assignment of the two feeder options. Transit trunk-line networks are laid-out in hybrid fashion, as proposed in Daganzo (2010). Transit lines thus form square grids inside city centers, and radiate outward in the peripheries. As in Daganzo (2010) and other studies, a set of simplifying assumptions are adopted that pertain primarily to the nature of travel demand. These enable the formulation of a parsimonious, continuous model. The model produces designs that minimize total travel costs, and is ideally suited for high-level (i.e., strategic) planning. A similar model is developed for systems in which access or egress to or from transit can occur solely by walking, or by walking and riding fixed-route feeder buses in combination. The shared-bike and feeder-bus models both complement Daganzo's original model in which access and egress occur solely by walking. Comparisons of these feeder options are drawn through numerical analyses. These are performed in parametric fashion by varying city size, travel demand, and economic conditions; and for trunk services that are provided either by ordinary buses, Bus Rapid Transit, or metro rail. Designs are produced for cases in which shared-bike and feeder-bus services are made to fit pre-existing and unchangeable trunk-line networks; and for cases in which trunk and feeder services are optimized jointly. Outcomes reveal that shared-bike feeder systems can often reduce costs over walking alone, with cost savings as high as 7%, even when the shared bikes are made to fit a pre-existing transit network. Shared-biking often outperforms feeder-bus service as well. We further find that the joint optimization of trunk and shared-bike feeder services can reduce costs not only to users, but also to the transit agency that operates these services. Savings to the agency can be used to subsidize shared-bike services. We show that with or without this subsidy, shared-bike systems can always break even when they are suitably priced, and jointly optimized with trunk service.