I don't have any tips because I wear washable spray dyes, but at least you didn't use red then people would think you forgot sunscreen. People are stupid and would judge you no matter what, so red would be worse I would try Vaseline.

Rubbing alcohol will help get the die off your skin

Isopropyl alcohol in a cloth will get it off

You're supposed to rinse it so it doesn't get on your body.

Thats why you wash your hair in the sink after dying it. YDI.

Ydi or coloring your hair blue in the first place! Common sense would think that the dye would run.

Try vinaigrette it worked getting the red dye off my head and neck

try baby oil, that usually works.

Hand sanitizer helps get color off the skin. But this is why you should always just get it professionally done to begin with.

Honestly if you knew anything about doing your hair you would know you don't "dye" it you color it. Second the color washing from your hair would not color your skin. Unless you stood there like a lazy person. If you actually showered I highly doubt that your skin would have been blue.