How does one disable the 'BellSouth Accelerator ?

unless you can right click on the icon it should have a disable option…
OR
As I was directed by a Bellsouth Technician at: Bellsouth Tech Chat:
http://home.bellsouth.net/csbellsouth/s/s.dll?spage=cg/contact/chat.htm

They recommend that you try uninstalling, then reinstalling the software:

•    Click on 'Start'.
•    Go to 'Programs'.
•    Go to 'BellSouth Accelerator Technology'.
•    Click on 'Uninstall BellSouth Accelerator Technology'.
•    Download the update at:
http://accelerator.bellsouth.net/update . Run this program
to clean the old settings out of your computer which is blocking the download.
(When you run it, it dosen't appear to do anything. This is normal, it just
needs to remove a few old settings and it does it faster then you can see.)
•    Try to download the product again at:
http://accelerator.bellsouth.net

If this does not resolve the issue, completely uninstall the program. There are
currently issues within the program. We recommend that you check back with Bellsouth,
as they will be releasing new versions of the program as improvements are made.