Pending a reply from someone who knows the answer this may help.
I have Joomla installed and I have Gallery2 installed (the latest one click installs).
They have both worked okay for some time.
So I had a go at doing what you want.
If you have not already have a look at this page/site. :-
What I did was to download the bridge component zip file (83kb) for G2 at SourceForge:-
(this is for Gallery 2 2.1.x only which is the DreamHost version)
Then going into the Joomla admin page I selected the installer/component page and uploaded and installed the zip file (from my PC).
Then from the Joomla Admin components option you will see the component G2 has been added. Enter the config section and add the 'server' path to the G2 location and the URL to the G2 location.
At this stage I have not changed any other settings but have just added a button to the Gallery on the front page.
This works okay and I can bring up the Gallery2 front page embedded in Joomla.
I get a 404 error when trying to enter a gallery but I think that is just something not configured yet. I also seem to think that the albums in my Gallery2 were not set up as public when I installed G2 a long time ago
But at least the component seems to work so it is just down to fine tuning now.
See how you go for now.
Opinions are my own views, not DreamHosts'.
I am NOT a DreamHost employee OK!! :@
You act on my advice at your own risk!