£140 is cheap. The airport taxis charge £165:
http://www.atmairport..._en/popup_ter_isl.php
Your alternatives aren't great, but here they are:
There's a bus to Fethiye (1 hour journey)
http://www.atmairport...Dalaman_en/ulasim.php
From there you can get a bus to Antalya (3 hour 45 minute journey on the inland road = 'yayla yolu'):
http://www.batiantalyatur.net/?&Bid=212701
(Avoid the coast road service = 'sahil yolu'. It take 6hours 30 minutes!)
From there you should be able to get to Side fairly easily.
Alternatively, if you drive, it would be far easier to rent a car. These companies are represented at Dalaman Airport:
http://www.atmairport...laman_en/rentacar.php
Another way to get there would be to fly to Istanbul and then onto Antalya, with Turkish Airlines. However that would depend upon when you land at Dalaman. The only reasonably priced flight combination (203TRY = approx £90) departs at 1350 and (after a 2 hour 25 minute stopover in Istanbul) arrives in Antalya at 1850:
http://www.thy.com/en-UK/
Chris