Adaptation of existing infrastructure is a response to climate change that can ensure a viable, safe, and robust transportation network. However, deep uncertainties associated with climate change pose significant challenges to adaptation planning. Specifically, current transportation planning methods are ill-equipped to address deep uncertainties, as they rely on designing responses to a few predicted futures, none of which will occur exactly as envisioned. In this paper, we propose using dynamic adaptive planning (DAP), an emerging general strategic planning method, to account for deep uncertainties by building flexibility and learning mechanisms into plans that enable continuous adaptation throughout implementation. This paper first reviews uncertainty in general, introduces what is meant by deep uncertainty, and then introduces DAP. Then, DAP is applied to a case study of the Oakland approach to the San Francisco-Oakland Bay Bridge, which was initially assessed under the 2010-2011 FHWA Climate Change Vulnerability Assessment Pilot program, to illustrate how DAP could be applied as a response to climate change in the context of evolving transportation infrastructure adaptation planning practices in the United States. We conclude that DAP is well suited to account for the deep uncertainties of climate change in transportation and infrastructure planning, and provide suggestions for further research to better apply DAP in this field.