For anyone looking for a way to mount their Transformer to Linux Mint, I wrote a script to automate the process of configuring your machine to allow you to browse/modify files on the tablet's SSD. This will probably also work on Ubuntu, but I have only so far tested it on Linux Mint.
Download the attached file, and run it.
Edit: Connect your Transformer to your PC before running.
Edit 2: You only need to run this script once - not every time you connect the tablet to your PC.
Hit the thanks button/comment if this worked for you. If not, also comment and I/someone will probably help you out. Also, if anyone tests it on Ubuntu successfully, be sure to comment and let people know.
Note: All configuration files are backed up in the script before changes are made. You can always revert safely.
I'll throw in the ever so popular "use at your own risk" for safe measure.
June 29: Updated script uploaded.
-Removes an unnecessary comment pushed into fstab in the previous script
-Already executable. Just run it. [Thanks MagnusRagnarok for the idea]
-Packed in 7z from Linux Mint this time as opposed to in zip format from the TF, for [hopefully] universal accessibility.
-md5sum 615f2bfa820ee9ac8ea2c967149a2f03 TransformerMount2.7z