I propogated a begonia (don't know the variety) in water. Moved all plants to a small (6 ") pot afew months ago. But, they're all somewhat "leggy" with no signs of blossoming.
Sounds like they need lots more light and some food. Move them outdoors for summer (no hot afternoon sun to begin with). Acclimate them to more light over a week or two. A few hours of morning sun or late evening sun should help tremendously.
Feed with diluted water soluble fertilizer and/or slow release fertilizer.