2.01 adds Master status to professions, which allow you to reach up to 375.
For Primary professions you need to talk to a Grand Master, which are all found on outland (most are in Honor Hold/Thrallmar), and thus require TBC.
For Secondary professions you need to learn books. The books are all sold on Outland as well, but they're BoE, so you can have people selling them to you. For 1st aid, the new 'recipes' are also from books, so you can learn those as well. For cooking, most of the new meat recipes are from bop recipes you can buy from reputation quartermasters, so not available to pre-TBC users, but most of the fish recipes can be bought from vendors and thus given to pre-TBC users.
Note that you can level quite a bit on old maths, but eventually you need TBC maths which might be a tad expensive to come by.