Anderson's book should also be my recomendation. Although it is not finished (and there are some minor mistakes in it), it covers many different topics(and bibliography), and collects many results (and bibliography) that are hard to find elsewhere.
As for the Czech school, there is Krupka's review Global variational theory in fibred spaces, (2010), and Krupkova's Variational Equations on Manifolds (2009), which include a complete list of references inside.
Another interesting reference is the section devoted to variational caluclus in Aldrovandi's book An introduction to geometrical physics.
