I have tried 5 different methods to clean up soap with soda ash (each method is followed by drying/polishing using a microfiber cloth.) Here are the methods, in no particular order.
Dip in very hot water
Spray with alcohol & wipe with cloth to dry
Rinse off with steam (wear heat resistant gloves)
Rinse off using vegetable glycerine
Plane/cut/scrape it off the surface
Obviously, for fancy tops or decorative designs atop soap (piping, or soap dough additions), most of these methods will destroy the art work, so in those cases, you pretty much have to live with the ash.
For soda ash removal, all of these methods work, but I only tried the glycerine once, and it doesn't work any better than alcohol or plain old hot water. The steamer process works, but requires extra equipment, set up, tear down, etc. that I don't need if I use alcohol or hot water. I always have a spray bottle of alcohol in my kitchen and I always have very hot water available. Wearing heat resistant gloves requires extra equipment if you don't already have a pair (I bought some especially to use with the steamer, because the first time I tried that method I burned my hand.