What operating system is running on your desktop? Most likely your mp3 player is using a windows based filesystem, such as, ntfs. There is a utility in Linux that helps read ntfs filesystems call "ntfs-3g". It might be named slightly different on Ubuntu. I run Debian Sid, which Ubuntu is based and the program is called ntfs-3g. Take a loook in your Add/Remove Software application (Package Management) and see if ntfs-3g is installed. Or, in a terminal, type:
apt-cache policy ntfs-3g
And the result will tell you if it's installed or not.
If it's not installed, install it from the package manager, and see if it helps. If that is not the problem, give us some more infomation about the mp3 player (Brand, model number etc.) and tell us about the desktop that it's working with. The fact that is appears then bombs out when you try to mount it is curious. I would suspect that it wouldn't show up at all if ntfs-3g wasn't installed, but, most of my installs come with ntfs-3g, and, I've never had your particuar problem.
It also might just be a configuration problem. I'm not an Ubuntu user (some here are), but, if there's an option in the settings for automount of removeable devices, make sure that is enabled. That may make a difference.