Move site across server
You can directly schedule Site Migration across server from a site's dashboard.
For moving your site to a dedicated server from a public bench group
Use Change Bench Group option to move the site to a private bench group
Follow the below steps to move the site to your dedicated server
To change the server for the site go to your site Dashboard>Actions>Change Server.
Select the server you want to move to (Your team should own the server).
If the selected server isn't added to the bench group add it by clicking on Add Server to Bench Group.
Click Migrate Site to Server if the target server is added to the bench group and the Site Migration will be done in the scheduled time (or leave it untouched if you want it to start immediately).