You could walk, it's only a little over a mile but it is uphill.
If you don't want to walk the entire way you could walk out to Via S. Teresa degli Scalzi and pick up either the C63, C67, R4, 168, 178, of 460 buses, all of which have a stop just across from the entrance to the San Gennaro catacombe.
If you walk, be sure to catch the Rampe San Gennaro dei Poveri street, as the Via S. Teresa degli Scalzi is on a much higher level than the other streets (Naples really taught me about considering different terrain levels while navigating with maps). There is also an elevator on Via Sanità, but back in 2014, I've never seen him in service, I think (though it might be my memory playing tricks on me and in any case, maybe it has been repaired).
Yes, you do have to pay attention to that in Naples. Intersections that look normal on a map can actually be one road that's 20 or 30 feet above the other one. In this case you'd need to walk a little bit south (to Vico della Neve) or north (to San Gennaro dei Poveri) to find an actual intersection.