I don't think there is anything native to SSIS for this and I'm not sure this is really an SSIS task as much as a coding task. But it doesn't mean you can't write a CLR function or have another external app of some kind to do this.

However, how to do it really depends on what URL shortening service you are using. There are many of them. Your example is using Bitly and they do have an API available which can be used to expand a URL. Most of the other services do as well and there are examples up on CodePlex for some. Some of the APIs require you to provide a login, some require registering you application with them, some require money, some have free examples, etc. How it's done really depends.

Sue