You will need to turn your path into a Clipping Path.
You select your Working Path in the Paths palette and, from the fly-out menu in that palette, first choose: "Save" (it will become "Path 1")
and then choose: Clipping Path…
and in the next dialog, select "Path 1" .
Save the file as an .eps.
[There are shortcuts for doing this, but this should suffice for now.]