I've tried looking through the free AOL e-mail service to work out how to export contacts, but it seems that they're not playing ball.. you can only import address books.
Just to check, is anything actually pressing you to stop using the AOL e-mail or is it just the standard
Internet e-mail service? (Whose use isn't dependent on the ISP you use)
If you really must change, then all I can think of to lessen the burden of copying and pasting every single address is to address a single e-mail from your AOL address to all of your contacts asking them to reply to your BT address so you can add them.