Here you go...
http://bestplay3.www.megashares.com/myms.php
The Burning Crusade Beta Patch v.5991 to v.6022 ->
http://bestplay3.megashares.com/?d01=a03e024 (272.67 MB)
The Burning Crusade Beta Patch 6022 to 6046 ->
http://bestplay3.megashares.com/?d01=27ac026 (21.16 MB)
The Burning Crusade Beta Patch v.6046 to v.6052 ->
http://bestplay3.megashares.com/?d01=c2f75b9 (10.31 MB)
There are all enUS patches, these three will take you from fresh to newest (I think).
From Justinkk on Blizzard's Beta Forums...
"All I stated is that it is not technically against the ToS/EULA. Of course when downloading a patch from an external source you should take the necessary precautions as the file could potentially be altered. Please be sure to scan all the files with an up-to-date virus scanner before running.
You can also use the Blizzard Downloader to verify that the file was not altered. You can do this by moving the downloaded patch to your Burning Crusade Closed Beta folder. Next run WoW-2.0.0.5991-to-2.0.0.6022-enUS-downloader.exe and it will verify that the file was not altered in any way. If it has been altered please do not run the file, and immediately delete it from your system."