It's not too early if you have some kind of light source, like a flourescent fixture or access to a greenhouse later. I start mine indoors around this time or a little earlier. but I move them to my greenhouse in mid April.

It sounds like you didn't if they got leggy before. It would cost you less than $20 to get a plug in flourescent fixture.

A friend told me this method of starting them and it has worked for me for a few years now. I start them in the container in which they'll be going outside. I put a few inches of soil in and then the begonia tubers, just covered. As they start to sprout, cover with more and more soil until, over the weeks, you're at the right level. They don't get too leggy that way. Oh - i usually have the containers hung in sunny windows, and the overflow go under lights.