I usually identify ash trees in the forest first by the bark, then by checking for the oppositely arranged compound leaf and the friendly leaflet shape they usually have. Since this is a bonsai, it of course isn't going to show the same mature furrowed bark a forest ash would. That being said, that definitely looks like an ash leaf to me. In the one photo with your finger in it, I'm pretty sure I see oppositely arranged leaves. Another good case for ash. Also, the fact that they said it was an ash gives a good case for ash. =]
It seems that the most common ash used for bonsai is Fraxinus excelsior. That specie is native to Europe. I'm only familiar with ash species in the U.S. Not that you couldn't have a European ash somewhere else! Looks like Fraxinus excelsior has pale undersides to the leaflets as does white ash. So it could also be white ash, which from a quick google search does seem to exist. Probably the determining factor now would be your location and the origin of the bonsai.