Some species are regarded as having a very wide genetic base and some less so, which commensurately signals that a bottleneck has taken place, and that diversity takes a while to be amended. You can make some measurements on when the species population may have been small in the past, although some of those kinds of study have been found to be very misleading, because populations can interbreed cross species, like neanderthal, which brings up a much more complicated picture to the genetic bottleneck model, and makes some research results seem over stated. In otherwords, recent studies in that field by trained scientists have found errors.
here are some measures of recent or distant small populations: http://www.tiem.utk.edu/~gross/bioed/bealsmodules/bottlenecks.html
Directional selection generally is related to a considerable force on the population which changes is population dynamics and can therefore amount to a bottleneck, or which selects only one type of adaptations from a population in a region, which is then transferred to the rest of the population by a less sudden kind of evolution, which amounts to a semi bottleneck with a wider base. different branches can converge from 40,000 generations distance in speciation, or in 50, which means that it's difficult to gauge a bottleneck without very complete studies.
Take for example moths at the beginning of industrialization when coal was used in large amounts. They noted that the same species of moth could change from light to dark to blend in with the background, and that the white moths dissapeared.
That illustrates a kind of bottleneck as a result of directional pressure, although the species may have been far from failing, it just underwent a bottleneck to some degree.
Bottleneck genetics is very complicated and difficult to understand, because they have quite a strong effect on the genetic base of the animal and it variability. and because low genetic variation implies a range of mutations which can be fitness or protein malfunctions or dynamic changes depending on the kind of bottleneck.