Frankly these days many bar soaps are formulated to be just as non drying as any shower gel. The soap dries out the skin sales pitch is old and out of step, but as long as people still believe it then the pitch people will continue to say it.
Dove is great and because it's been around so long she will know the brand and won't feel like you're trying to put anything over on her. Another inexpensive option which you can easily find at grocery and drug stores is Kirk's Castille Soap. Castille soap originated in Italy and its ingredients are pretty simple -- and none of them are harsh detergents.
There are some more expensive perfumed options too (Caswell-Massey, L'Occitane, Asquith & Somerset), but let's save those as a nice stocking stuffer for MIL.