WD MyBook appears as read-only My WD MyBook Essential with USB 2.0 appears with read-only permissions. I set the drive up on my old Vista machine, and when Vista began crashing, I switched to Ubuntu. I still have the Ubuntu machine, but started using a Mac. 

The drive is encrypted through the WD SmartWare program. While I can unlock the drive, and access files, I can't write to it from either machine.

Is it possible to make the drive writable from my Mac without losing data?
If the drive started out on Vista I'd assume it has been formatted using the NTFS filesystem. You can confirm this by selecting the drive in the Finder, right-click it and selecting "Get Info" from the menu. The Info window will list the format under General.

Unfortunately on Macs by default NTFS is always mounted read-only.

There are a number of options to enable write access on OS X. There are commercial products like Tuxera NTFS for Mac  and Paragon's NTFS for Mac OS X. There are also free open source solutions like NTFS-3G and if you are confident in using the Terminal you can use something like brew to install NTFS-3G.