I haven't used Textmate in a long time, and didn't use it for Perl even then, but there is a menu item "Perl" under the "Bundles" menu. If you have a perl script open, put the cursor over something such as "strict" and click on the Perl bundle item "Documentation for Word" and up will come the perldoc.

I think its a default bundle, but if you don't have it use "GetBundles" to get it or look on Github. Hope that works.
Good luck.