Richard's second suggestion would be my first.
Create a new sequence using a smaller frame size. Create your titles on that sequence, letting them scroll all the way to the top.
Then take that sequence and nest it into your original sequence. Since the frame size is smaller, use the Motion Effect's "Scale" parameter to put the nested titles at the bottom of the larger frame. Now they will not reach the top of the larger frame and give you the effect you want.
Tip: Put the original video into the new sequence as well to help you with timing. Then when finished, delete (or hide) the video track so that it does not come over when you nest the sequence.