If you take your time wrapping it and keeping a little bit of tension on the tape while wrapping the bars, you shouldn't have much issue. Also avoid doing any thing like a harlequin wrap until you have some more time wrapping bars. After the first couple of times, it will get easier. I learned via trial by fire, wrapping the bar on my bianchi with brooks leather bar tape.
__________________
Appreciate the old bikes more than the new.