Yes, the bike mount works with the new Vista HCx. Just got mine a couple of days ago.
The HCx ships with a screw-on adapter in the box that allows it to fit the existing bike mount.
The bike mount comes with a back cover for the GPS that you won't use with your HCx. You don't replace the back cover, you attach the adapter to the standard back cover. I presume that they just made the updated style standard on the HCx.
Just be sure you don't lose the adapter that ships with the HCx! (Mine was loose in the box, and I wasn't sure what it was. Took me a few stressful minutes to figure where it had gotten to after I got the bike mount!)