How does one put a nighthawk X4S in bridge mode

> [...] nighthawk X4S [...]

   Not a model number.  Look for "Model" on the product label.  C7800,
perhaps?

> I have no idea how to put this cable router in bridge mode and I don't
> even see the opinion to do so.

   It's pretty effectively hidden.

   Visit http://netgear.com/support , put in your (actual) model number,
and look for Documentation.  Get the User Manual (at least).  Read.
Look for "Connect Your Modem Router to a Router After Installation and
Activation".  It's not clear (to me) that that does the whole job
(disabling the radios, and so on), but it might be as close as you can
get.