This ^^^^

Also known as Friction Tape and Grip Tape.

It was also the original ELECTRICIANS tape (not electrical tape) through most of the last century, until sometime in the 1960 era I believe when 3M introduced the vinyl electrical tape we know today.Vinyl tape doesn't work as well on the handlebars in my experience.

It is a CLOTH tape ( I've only seen it in a black color ) that is TACKY ON BOTH SIDES ( a bit stronger tack than a Post It note ).

You can find it at any big box home improvement store in the same general area as the vinyl electrical tape, for a very reasonable price ( approx. $1.50 a roll last I bought some... admittedly many years ago ).

The stuff they sell in the big sports goods store is basically the same but premium priced (and possibly in assorted colors).