As far as I know, Bragg diffraction happens for incident particles which are free; for example free electrons or X-ray are Bragg-reflected under the special conditions. Why the Bragg diffraction happens for electrons which are not free in a crystal?
Bragg diffraction happens for WAVES. Waves can be of any nature and spread in any medium. Electron wave in ion's lattice is a WAVE with ions as diffracting screen.
If we consider the diffraction classically, incident waves are in direction of [itex]k[/itex] and reflected waves are in direction of [itex]k^\prime[/itex] and [itex]G=k-k^\prime[/itex]. But for electrons in crystals direction of motion is not direction of wave vector.