Fossy's sugestion would seem to be the best. First wipe with damp cloth then work in small amount of washing up liquid or Swarfega(Fairy best if using washing up liquid). Rinse throughly then park bike in sun to dry.
After using WD40 to try and clean my bar tape I would be careful with any solvent based product and if used, use it sparingly, WD40 removed the adhesive on my tape allowing it to just turn on the bars, it took about a month before it stuck itself back down again.
In the end I gave up worrying about my white bar tape getting dirty as its unavoidable out on the roads, when you start getting your hands dirty with replacing chains, repairing punctures, food etc