Keep in mind, BitBucket utilizes Mercurial for Source Control, NOT Subversion. Granted, Mercurial might be a nice step up to use and learn, but that's a discussion for another answer. Also, BitBucket will limit you to one, free, private repository.
I've used Assembla in the past and they've been okay, nothing particularly special.
There is also the option of running your own Subversion server, which can be extremely easy on Windows by using VisualSVN Server. Sign up for a dynamic-dns account, and you can easily point a hostname back to your home computer.
Lastly, I just noticed, but my Dreamhost hosting account comes with the ability to create Subversion repositories, and it's pretty cheap and comes with a domain name.