If you want nice cloth buy hockey tape... seriously.
It has a high thread count, adhesive backing (that is easy to remove), is tough as hell, and with a few coats of shellac will last indefinitely.
The drop bars that were on my old Pug also still look as good as the day 1 which was over 20,000 km ago and cleaning up the bars is easy as grease and grime just wipe right off... just avoid spilling alcohol on your bars as this is the solvent in shellac.