I'd agree with Nickls regarding Corn n Oil being the cocktail de force for falurnum. The best I've had came from the legendary Murray Stenson, when he was at the Zig Zag Cafe in Seattle. If I recall his was Made with Blackstrap Rum, falernum, a couple of squeezes of wedges on the rocks. I had faith that it would be amazing since I've never had a miss with his precision poured concoctions. Sure enough, I was thoroughly impressed with the drink.
I don't recall if Murray used bitters, but recipes that I've seen do call for it.
I've also had the Ninth Ward twist found in Difford's guide, which calls for bourbon and elderflower liqueur. Nice pairing of bold bourbon Flavors with falunurm.