Using the official Python bundle I seem to only get completion on commands, not lookup of methods on the object at the cursor.
You'll need to install both ropy at a system-wide level and the textmate-ropy bundle to get this, but it worked for me. To install ropy, just go to a terminal prompt and type
sudo easy_install ropy
Then to install the textmate-ropy bundle, you'll need to check it out of Subversion, apparently. Again at the shell prompt:
svn co http://textmate-ropy.googlecode.com/svn/trunk/ textmate-ropy
(I presume you know Subversion, but if you don't, that creates a "textmate-ropy" directory.) Then just double-click on the Ropy.tmbundle file that will be in the textmate-rope directory you've created.
The autocompletion command for TM-Ropy appears to be ^P; ^] will take you to the definition of a method.
Having said all this, this is actually the first time I've used Ropy! I tend to keep a Ctags file up to date for my projects using the "TM Ctags" bundle, which gives me the ^] equivalent for nearly all languages. (There are two Ctags bundles, but in my experience the other one doesn't work.) The autocompletion that this bundle provides looks a little barebones to me but I guess it could be cool.
I will say that if you get used to Emacs -- I never quite have -- it does do really well with dynamic languages like Python and Ruby. I've tried to switch away from TextMate to several other coding environments but keep ending up back here, though; despite my frustration with a few misfeatures and concerns about the program's future development status, once you really start taking advantage of its power it's awfully hard to leave.