Start from the bottom and go outwards towards as you make your way to the stem. Easier to cut it and finish it with electrical tape. I find it a pain to go the other way and cram it into the drop bar hole with a stop/barend.
I know on the older vintage rides or the randoneers like to tape from the bottom and finish it off with twine and shellac. Looks pretty sweet..but probably not so nice on a modern road bike.
EDIT: just had a look at your ride. I think the twine thing would look pretty sweet on this. Poke around rivbike.com if you are interested..