This http://manual.b2evolution.net/Move_my_installation is the manual that regards your issue. If i'm correct, you'd better do the database stuff first and then install your version of B2o, the same as you had on your previous blog. There is a possibility to move the database after you've installed B2o on your new server. Look at these http://manual.b2evolution.net/Import_posts_and_comments in the same manual.

Good luck.