Hi Karen,
I started some Bada Boom & Bada Bing begonias last year. The seeds were pelleted so it was easy. I had them under lights along with everything else for 15hrs per day. They do require feeding quite early. They are very tiny too and takes a few weeks to really get going.
The 1st tray that I seeded last January did not do well. Poor choice in medium (note do not use cocoa choir..zippo for nutrition.
I thought I would try again with different soil in March and they did awesome. I used Premier Pro-Mix BX and fertilizer with fish fertilizer. I had bought a few bedding plants in late May and the ones that I started from seed were the same size or bigger than the ones boughten in the 606 (6pack).
Stokes Seeds has a get "how to" explanation for Fibrous Begonias. I will definately seed them again and will use the BX soil mix with Fish fertilizer.
Hope they do well for you