Saw someone doing this in a game last night, decided to try to replicate it.
Works with all 3 Crossbows.
After firing, “sheathe” your crossbow(bring it down from the shooting position), run in whatever direction you choose(I only tested going forward) and press reload. You will keep moving at a slower pace, and you will reload.
Movement feels faster when using the crossbow/heavy crossbow, but that may be because I used the light crossbow first in order to practice it.
This is on LIVE servers, not BETA. I tried it out in versus bots.
I was also able to stand still - start reloading and then start moving. I think the video shows it once with the heavy crossbow.
EDIT: Apparently this has already been fixed in the upcoming patches, so you can disregard this post.