Both are acceptable. I prefer the second option ("Charles’ bike"), but the first option is also fine, and most academic style guides recommend it. If you're forming a possessive for a PLURAL noun, you should just use [’], not [’s]. For example, if there is a bike that belongs to two kids, you should write "the kids’ bike." Don't add an extra "s" after "kids’." However, if the noun is singular, like "Charles," you can form the possessive with either [’s] or just [’]. Academic publications usually prefer the format "Charles’s bike," but other types of media, like newspapers, usually prefer the format "Charles’ bike." Neither one is wrong.

Hi there, I would use #2: Charles’ bike.

When constructing the possessive forms of nouns in English, the apostrophe usually goes before the "s" for singular nouns and after the "s" for plural nouns. This case is an exception because "Charles" is a proper noun that ends in an "s."