I've single or double wrapped old inner tubes, cut into strips, as the base layer, then covered that with good bar wrap. Inner tubes alone tend to make a sooty mess on the hands and hoods.
Also, Arundel Synth Gecko is really soft, rubbery and grippy, and easy to rewrap and reuse indefinitely with care. But it's not their best looking bar wrap. Like Fizik and others, Arundel has a lot of good looking textured and heavily padded bar wrap.
Back in the 1970s I used foam rubber pipe insulation to wrap my handlebar for century or longer rides, but it is odd looking and can twist around if not secured really carefully. Cheap and worth a try but nowadays I prefer the inner tube base layer trick under cosmetically appealing overwrap.