Bitly doesnt offer this service in their free plan. They consider it to be a premium feature and have made it available only to their paying customers.
Another reason for this is to prevent spammers from abusing Bitly. "Bitly has built a sophisticated system to prevent and reduce the impact of spammers using our Bitlinks (Bitly links) to send malicious or phishing content. However providing the functionality for spammers to build trust in specific URLs then easily redirect them to malicious content is a challenge we don’t currently want to tackle." - Dan Touchette (Director of Product Management at Bitly)