I’ve just managed to get the plugin working. As Alex King says above that this only affects users “incorrectly entered their username and API key” I thought that this was worth looking into. Although to the naked eye my username and API looked absolutely fine there was a blank space after my API key (a result of copying and pasting from my bit.ly account). I deleted this blank space and published a test post which worked perfectly and included the shortened url. Really pleased that this is now working as I use it on 4 blogs. I hope that this solution works for others.
Best wishes,
Lee