How do you transfer music you bought on the iPhone to the computer?

You can do that by connecting the iphone to your computer using a usb cable.

Jailbreak it, download openssh from the cydia store, download winscp on your computer. connect to your ipod, the username is root and the password is alpine. navigate to /private/var/mobile/Media/iTunes_Control/Music on the ipod. Copy over all the files you see to C:\Users\Your Username\Music\iTunes\iTunes Media\Automatically Add to iTunes\

$100 says I lost you at the second thing I said.