This is the first link when I googled 'free bitmap vector'
http://graphicssoft.about.com/od/bitmaptovector/
I love how none of those are free, despite the search term :P
Another link from further down
http://www.masternewmedia.org/2004/02/28/autotracing_how_to_convert_bitmaps.htm
Their list includes an open-source tool
http://potrace.sourceforge.net/
Honestly though, this isn't a task that is really good for automating. You'd be better off tracing over your drawing by hand in a vector illustration tool. Also, what sort of cleanup do you need for your lines? They look pretty clean to me.
http://graphicssoft.about.com/od/bitmaptovector/
I love how none of those are free, despite the search term :P
Another link from further down
http://www.masternewmedia.org/2004/02/28/autotracing_how_to_convert_bitmaps.htm
Their list includes an open-source tool
http://potrace.sourceforge.net/
Honestly though, this isn't a task that is really good for automating. You'd be better off tracing over your drawing by hand in a vector illustration tool. Also, what sort of cleanup do you need for your lines? They look pretty clean to me.