For my latest build I was going to use an aero lever, backwards, underneath a bullhorn bar. I'm sure I'm ******** but what is the best way to wrap the bars around this?

There isn't much of a trick to it. You use that little piece of tape to cover the clamp where the lever attaches to the bar. When you reach the lever, just wrap around it. The little piece of tape should cover the gap created if you are careful. When you get two wraps past the lever, stop to inspect your work for gaps.

Edit: Also, when you make the wrap around the lever, the tape kind of makes a V (if that makes any sense) with the small bit of tape filling the middle.

Is there an issue with not having a hood?

Depends on what you mean by "issue" The hood helps cover up some of the inevitable gaps at the top when you go around the lever. I have never wrapped a bar without the hoods, so I have not been particularly careful to avoid little bits of silver at the base of the lever. Go slow and pull the tape tight and you should be able to get it pretty much covered.

There is no functional issue to having a small gap here, though. It used to be the racer look for roadies to leave the gap there.