I'd like to be able to post to and get information from a Linux command line (and therefore be able to write little bash scripts to work with projects) similar to
gcalcli for Google Calendar.
Is this possible with Trello?
Trello does have an API which is documented here. Using that you should be able to write scripts to perform any action it supports.
It doesn't look like anyone has written a bash interface as yet, however you could possibly make a Python based command line tool based on the libraries listed on that page.