You can't transfer files from one host to another via FTP. You'll need to download them to your local machine from BH, and then upload them to DH.
When you log into DH with FileZilla, you should see a structure that looks something like this:
Anything you drop in that last directory will be visible at "domain.com"
"ftpuser" is the user name you set up in your DreamHost panel.
I'm not sure if there is a way to transfer files from one host to another via the command line. (Worth checking into if the amount of data you have to transfer is large.)