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For $2 get some Walmart glass cleaner. For $8 get some H-D denim spray cleaner. Glass cleaner works well on chrome too. Dish soap and warm water for real dirty bike. Cheap maintenance...
I'm on my second Black Denim bike, been using the Denim cleaner since the first. I've never had any issues with it. Use mild dishwashing solution to wash, blow dry the bike.