Build America Bonds Extension for Rural and Urban Transportation and Highways Act of 2011 or the BABE RUTH Act of 2011 - Amends the Internal Revenue Code, with respect to the Build America Bond program, to: (1) extend until December 31, 2014, the authority to issue such bonds and the authority for payments to issuers of such bonds (2) reduce the percentage rate of payments to issuers in 2011, 2012, 2013, and 2014; (3) allow refundings of currently issued bonds; and (4) allow the use of Build America bonds to fund capital expenditures for levees and flood control projects.