You may have noticed that Twitter have started using their own URL shortener. Your links will now appear as http://t.co with a reference code after the t.co.
“If you’re wanting to shorten links to share with others, please see this help page on using URL Shorteners. You can continue to use a URL shortener to shorten links, and any tracking metrics (like those from bit.ly) will continue working as before.” Twitter
Good news folks! Your bit.ly links will continue to work with Twitter.
You can still use a URL shortener (like bit.ly) to shorten and track links.
If you don’t know how to track click throughs with bit.ly set yourself up a free account. Use it to shorten your links. Share. Track. You can then see how many people clicked on it by adding the unique shortened link followed by + to see link analytics.
You can read more about new Twitter shortened links from the horses mouth. https://support.twitter.com/articles/109623-about-twitter-s-link-service-http-t-co