According to the Smart City Council, an adequate telecommunications infrastructure is vital for the success of businesses, industries as well as residents of future Smart Cities. However, currently available network technologies, such as 3/4G, GSM, LTE, and LTE-A, are rapidly reaching their limit mainly due to spectrum scarcity, cross technology interference and increased traffic demand. Such limitations are only going to worsen in the next years, due to the advent of Internet of Things technologies that are expected to interconnect billions of devices to the Internet. Dynamic Spectrum Access (DSA) has been proposed to overcome such limitations and exploit unused spectrum resources over multiple electro-magnetic spectrum bands. In this paper, we propose a DSA-based architecture in which DSA radio devices are deployed on the Smart City's urban vehicles (e.g., public buses, taxis, municipal vehicles, etc.), that act as data mules to gather and forward the various types of data. This results in a Delay Tolerant Network (DTN) in which devices can operate over multiple bands, if available. Given lack of research in efficient routing schemes for such networks, we first compare existing DTN routing approaches designed for standard (or single band) DTNs, such as Epidemic Routing and Spray and Wait, in urban DSA scenarios and show that they are largely inefficient. Subsequently, we propose extensions to these approaches in order to better exploit the availability of multiple bands in a DSA paradigm. Results on realistic traces based on the map of Lexington, KY, USA, show that the modified approaches improve the network performance, such as successful message delivery and network latency, however, at the expense of very high energy expenditure and message overhead. Hence, we conclude by pointing out that further research is needed, since significant performance improvements are still possible by designing routing schemes that are specifically tailored for DSA Smart City networks.