What is a good reference for a geometric version of Noether's theorem about Lagrangians, symmetries and conserved currents?

Another excellent book that does a proper job with Noether's Theorem is Peter Olver's Applications of Lie Groups to Differential Equations. 


Javier already gave some very good references. Let me just add one more if you are thinking about classical field theories: Demetrios Christodoulou, Action Principle and Partial Differential Equations. 


The simplest, most elegant and strongest version I know is, by far, the one in Aderson's book (see page 106 and ss.) He deals directly with the variational equation, with no explicit mention to the lagrangian. (By the way, it is surprising why this statement is not mentioned in Schwarzbachs' book!) 


A fairly modern approach which is usually attributed to Vinogradov (see also the last part of KosmannSchwarzbachs "Noether Theorems") can be found in the book Symmetries and Conservation Laws for Differential Equations in Mathematical Physics. The chapter on conservation laws and the Noether theorem is somewhat dense and requires a little familiarity with homological algebra and spectral sequences. So it might be good to complement it with another book (like Olvers). 

