I find if I stick my cuttings back in the pot they were cut from, they seem to root faster. the mineral/water content is the same and there's less adjustment (just my opinion).
also make sure you are getting a clean cut and I let mine air dry for an hour or so before putting back in pot. and yes, water rooting seems to work well for almost any of the begonias i've tried.

Thanks for that advice I will give it a try. I think I am a bit spoiled with things like Pelagoniums as they root so easily and quickly as you just seem to have to stick them in the side of a pot and forget about them. Begonias aren't just so obliging