The Hamiltonian theory for guiding centre and guiding centre bounce motion are made more easily accessible by means of an elementary method for derivation without the explicit use of Lie-transforms of Kruskal's general theory for nearly periodic systems. A number of previous results are confirmed concerning the correction terms of the standard lowest order theory. New results are presented regarding the validity of the form of the bounce motion Lagrangian as an all order result. The validity of the bounce motion equations for sufficiently long time intervals is also proven.