Semperflorens (aka ever blooming) are also known as wax begonias. They do seem to bloom all the time if they have lots of light, water when needed, and occasional fertilizing. You should be able to buy them at your local nursery when in season. You can order seed on eBay or other online stores.

There are also cane Begonias that are almost always blooming. One Begonia (called 'Castaway') that I bought in spring of '11 is now the star of about 6 pots, has started invading other pots, and I've given pieces to about 5 people. I don't have that much luck (or speed) with the wax ones. If you are able to show a pic, folks should be able to tell you which kind yours are, and how to multiply your plants, although an exact name may be elusive. There are a LOT of Begonias.