I am surprised to see the number of "wrap tops to ends" posts here; it may indeed be vintage, when Eddy's mechanics put a fresh wrap of pristine white tape on his bike each morning (taking longevity of the wrap out of the equation). That's what I did when I first had a "Disraeli gears" bike, but over the years realized that hand grasp lifted the edges of the tape wraps, so with further investigation I've developed a confirmed opinion is that it's better to go "ends to tops", starting on the underside at the bar's open end; and wrapping clockwise on the right bar (looking from the rear, the wrap direction being that your fingers follow when grasping the drop while riding) -- IOW, inside to outside over the top, and then changing direction at the lever (by wrapping a half turn around the outside of lever housing there) to change the wrap rotation to "outside to inside over the top". Repeat for left bar, symmetrically of course.

For bars that are wide (44 or 46 cm), I sometimes run out of tape such as Velox. 3 rolls can do the trick, though, with splicing at the brake hoods (as suggested by the Rivendell video linked-to below). Also, a double wrap at the tops, where I do most of my grasping, is an idea I would like to try (suggested, I think, by rhm ). I also put a strip of tape from one side of the brake hood around the bar and up the other side, as shown in the Riv video, to eliminate gapping there. I'm in favor of the twine finish at the center barrel, done pretty much in the fashion of Rivendell (also linked-to below).

Some of this "revisionist" handlebar wrap lore:

St. Sheldon, as interpreted by John Allen: https://www.sheldonbrown.com/handlebar-tape.html with an inconclusive (perhaps rendering it unnecessary) commentary at https://www.sheldonbrown.com/handlebar-tape.html#nerdy
I believe that the upshot of Sheldon's method, unfortunately obscured by John Allen's supposed improvements, is what I've described above. Allen's description "Sheldon generally started from the underside of the bar with the tape feeding outwards." is (to me) murky because he doesn't clarify whether "outwards" is "from the bottom" or "over the top". I believe it's the latter.

Park Tool (bottom up, with variations): https://www.parktool.com/blog/repair...tion-drop-bars

BF "mechanics" thread from a decade ago; opinions vary, but it seems to me the preponderance support the description above: Wrapping Handlebars - Which direction?

Rivendell video instructional: Wrapping Handlebars - Which direction?
Note that they start "outside to inside over the top" at the end of the drop, unlike the description above, and unaccountably cut the tape at the brake housing (while appearing to keep the wrap rotation WRT the tube the same). That accomplishes what's good for the tops of the bars, but means that when using the drops (which I seldom do) your grasp will tend to loosen or unwind the wrap, rather than tightening it, relative to the tape coming from the brake lever.
And finally, the twine finish: https://docs.google.com/open?id=0Bze...Y5MzBmMDJkMjU2 Now that's vintage!

None of this is critical, of course, compared to having something tractile on your bars, and as always, YMMV.