There is possible to auto join battlegrounds with a macro or even an addon.
However you can’t pick what battleground you can join. You can join on every loading screen meaning after you done a battleground and exit it will autoqueue to another battleground.
Since they removed the “battlefields” numbered like you saw Arathi Basin having 3-4 battlefields (Arathi Basin 1, Arathi Basin 2, etc) and you could join any of those, these days it isn’t possible from the default WoW interface.
The “battlefield” function still exist in the game even that isn’t showed.
Addon
For the addon download this one, unzip it into your addons folder. Download Autojoinbgs here.
It contains just 2 files, the .lua and the .toc, you can even check the codes, they have just a few lines.
You might try to modify it to autojoin bgs on every loading screen:
search for this line:
EventFrame:RegisterEvent(“PLAYER_LOGIN”)
and replece with:
EventFrame:RegisterEvent(“PLAYER_ENTERING_WORLD”)
Curently the addon will autojoin after you login, (first loading screen).
A full list of events here: http://wowprogramming.com/docs/events (useful for modifying the addon).
Macro
or create a simple macro and add this code:
/script JoinBattlefield(1)