Did you use the "Easy" one-click install or the "Advanced" once-click install for your WordPRess?
If you used the "Easy" version, there will be no code at all installed to your user space, as described on the install page:
If this is what you did, then yo will have to rely on DreamHost to update the application. I noticed when I tested it that the install claimed to be version 2.3.3, but i actually installed version 2.3.2 (which does need a "security patch" update).
The other information in my replies assumed you used the "Advance" WordPress "one-click" install, which would install the code in your subdomain's directory in your user space.