I'm just starting to experiment with propping violets- mine are in soil. Mine had roots when I checked after 2 weeks, I bet it's similar in water. I hope this helps!
I'd say 2-3 weeks. I've been propagating them in water for about a year now and they are all doing great. Make sure they have a lot of roots before you put them in soil, have lots of light, and keep the soil a bit moist.