How to distinguish between a genetic bottleneck and directional selection?
Population bottleneck will have genome-wide effect while directional selection will affect only the locus (and closely linked loci via a selective sweep). 

You can typically screen through the genome and calculate Tajima's D. Under a bottleneck scenario, Tajima's D will be expected to be negative everywhere. Under a directional selection scenario, Tajima's D would be negative only at the locus (and closely linked loci) to the one that is under selection.

There are of course a whole lot series of technics but the above is probably the simplest and most straight-forward (it probably lacks in power though).