About 4 weeks ago I got a deal with "Orient Thai" airways for a standby ticket to Chianmai for just over 1000bht. I had to go to the airport to buy the ticket but they had many flights and the process was quite easy. Once you get to Bangkok call in to a Travel agent and check if the cheap deals are still on. May be a little more difficult to get a seat this time of year but worth a try.
If flying eats away at the burget too much: a few years ago I took a night train with sleeper from BKK to CM. I found it pretty comfortable and cheap (especially because you save a night of accomodation). Open the curtain in the morning for some nice views.
Try to get your ticket a few days in advance. I believe around 300B should get you to CM. Look up Lonely Planet for more info if you're interested.