This is not possible at this time. You can archive a link such that it won't show in your Manage listings, but that won't prevent the link from being used by someone who has the link already.
Can I delete a bit.ly link?
We believe that being a legitimate shortening service means offering permanent URLs. Our users can feel confident that the bit.ly links they create don't unexpectedly disappear or expire.
How do I remove or archive links from my bit.ly History page?
You can remove a bit.ly link from your history by opening the Options drop down menu and selecting the Archive link from the choices there (the other choices are Share, Copy, and Edit). Remember that links archived from your public history are still permanently functional and will always redirect to their original destination. Note: for some related bit.ly basics, see: http://bit.ly/Ovnvf