Wrapping bartape from the bottom up makes sense but leads to issues about how to end the wrap at the top. Most people are familiar with using electrical tape to secure the end of the wrap however if the tape slips you will wind up with sticky black adhesive on your hands and then on most everything you touch.
While working as an electrician I have used heat shrink tubing for splicing and terminating large wire. However most of the heat shrink tubing in the larger sizes has adhesive inside that oozes out around the edges when you apply the heat to shrink the tubing. However a quick stop by my local electrical supply house netted me a lifetime supply of heat shrink tubing ($10) that is adhesive free and large enough to make tidy endings to my bar wrappings. This "termination" will not slip if properly installed nor will it leave sticky adhesive on my hands on a warm day and a 100 miles from home.
The details of this 3M product (FP-301) are in the pic below. The handle bar must be stripped. Cut two 1 1/4" wide strips of shrink tubing and slide them onto each side of the bar. Re install your brake handles and then wrap the bar as you would normally. Secure the end with electricians tape (wrapping in the same direction as the bartape) and trim away the excess bartape.
Next apply a little soapy water (or saliva) around the electrical tape and then spin the shrink tubing in the
same direction as the tape is wrapped while forcing the shrink tubing up and over the electrical tape. Next apply heat sparingly from a lighter (consider practicing on a loose piece of shrink tubing to see how much heat it can take before igniting) while being careful to keep the flame away from the bartape. Heat rises straight up so you may have to stand the bike on it's head to get the fllame to lick the shrink tubing at the right angle and cause it to shrink. Again a little practice might be in order.
Note: Shink tubing will shrink to 1/2 its' original diameter.
PS: I have also included a pic of an alternate use for shrink tubing. Covering cable crimps to prevent damage to the finish of your bike.