I do this a lot. Or used to before it became too much work to schlepp all those pots around twice a year :-) I think it is of benefit to grow a lot of tender bulbs in containers, as many of them require a good deal of soil heat to get started in spring as well as hot conditions to bloom well and containers heat up faster than inground conditions and you can move or place the pots to receive maximum sun and heat to encourage flowering.

The tuberous kind of begonia should be allowed to be touched by frost...a killing frost that does in their foliage. At that time you then remove the foliage and dig up the bulb, let them dry for a day or so in your garage or shed, then store them in your cool basement, away from light, away from heat, away from water. Make a note of which end is UP...store them in a way you know which is which. Then in March, bring them out and you can put them ontop of the refrigerator--there they might begin to grow a root. Whatever, pot them up, just barely under the soil surface...their tips might even be seen, water them, give them sunlight and pretty soon a little bit of fuzz shows on the surface....it might look like like mildew...but its not...its the bulb beginning to grow. Keep the soil damp...but not wet. Tuberous begonia is one of the slowest forming bulbs and it might be June or July before they come to sizable growth and bloom. The bloom they produce is worth the wait.

Some info that I have seen about these (and I have only overwintered them indoors to continue growing), was to cut them back to a couple inches just before a frost and then dig them and place them someplace to dry and finally store in a cool place after removing remaining dead foliage (some put them in dry peat and some leave them in a mesh bag with air circulation). There's a thread here and one here with some ideas. Good luck! They are pretty and the blooms (if yours managed one) are cool.

In the event any of you return to this topic, I just want to thank you. This is my first year growing these plants (I alternated them with Hosta in a ring around a tree in the center of my backyard). I was sent the bulbs free for ordering over a certain amount from a garden catalogue and basically planted them because they said "shade" and they were free. I'm absolutely in love with them. I've rarely seen flowers as beautiful as their leaves. I was also dreading the loss of them this winter. I'm so glad I can lift the bulbs and store them until spring. I plan on adding to the collection next year. Thanks again.