Securing a PCB board to a plastic casing - can I just glue the bottom?
Finding a glue that reliably adheres to plastics can be difficult. As such you just can't beat good old screws, spacers, and nuts for solid mechanical connection. 

In your case, since you want a direct transferral of motion information to the board from the box, I might be inclined to augment the screws with an epoxy filler that fills the bottom of the box and covers the PCB. As a bonus, the PCB will then also be protected from ay sources of moisture, contaminants etc.

BTW: If this is a motion sensor you will want the board attached to what looks like the lid in your picture (The bit on the right) since that has the mounting lugs, assuming you plan on using those. The deeper part of the box would then be the cover.