Search for href parameter in rich text field
Before Craft saves any keywords in the craft_searchindex table in the database, that content goes through a normalization process, including things like removing punctuation.

So the link "http://bit.ly/1eZFQMY" will actually get normalized to http bit ly 1ezfqmy.

If you really wanted to find all entries with bitly URLs in them, then using "http bit ly" should work.