All splices MUST be done in an accessible, approved box. You can't use what's sometimes called a "flying splice" where the two cables are attached and left to hang in the wall. In your case you'd bring the old BX into a metal junction box using the appropriate clamp. If there is a bonding strip in the cable, then that gets folded back under the clamp. If not, just use the clamp. Then you'd bring the NM-B (Romex) into the box, again with the appropriate clamp (which will be different than the one you used for the BX). The bare ground wire from the Romex gets attached to the box with a screw. Then make up your hot and neutral connections with wire nuts.

Thank you.

how would you ground the other end of the romax?

Is the BX the source of power? If so, that's Robert's answer. I would also use a metal junction box. It will have a threaded hole with a green screw to attach both ground wires.