Hi
"When adding text to a video clip is there a way to lock it to the video so that if the video moves, the text stays with it?"
Follow Borate's instructions if you just want to move both together and retain their relative positions.
If you want to fix them so further editing doesn't move them, that is they behave like a single clip......
LEFT Click the text track to select it.
Hold down the SHIFT key
Keep it pressed and LEFTclick the video track. Both clips are now selected and turn blue.
Keep the SHIFT key down and now RIGHT click the video track again
From the menu that comes up select to GROUP the selected clips.
The text will now be fixed to the video. Both will now stay together if one or other is moved or if any clips are added in front of them.
Note however, that if you split the grouped clips at a point that passes through both tracks or insert another into them, the grouping will be lost.
Nat