Your phrase "access that I have." is interesting. Are you bandwidth limited? Space limited? Shell limited? Explaining that would help clarify a better suited solution to your particular parameters.
In order to get the DB from one machine to the other your have to transfer the files. you could do this several different ways:
1.) Copy the whole mysql directory (after stopping mysql of course)
rsync -a main_host:/var/lib/mysql/ smaecond_host:/var/lib/mysql/
2.) Use mysqldump to dump the data base to a file then transfer said file:
On the main sever:
mysqldump > [local_file] rsync [local_file] secondary:host
On the new server:
mysql < [local_file]
3.) Sneakernet may be an option if you have physical access to one or both
If you are bandwidth limited rsync can be given the --bwlimit switch to rate-limit a xfer. If you are space limited - then you may have a much larger problem.