If you are looking to post your link to your Twitter account, you can do so from the Twitter tab in the BudURL.Pro product itself. Click on the tab an you will be prompted to authorize your Twitter account.
If you are looking for a third-party app to use, there are many that will alow you to post with your custom domain. For example, TweetDeck is one we recommend and will allow you to use your custom domain.
Here are instructions to use:
http://support.liveoak360.com/answers/224-can-i-use-tweetdeck-to-shorten-my-links