Much refers to the amount of money that one has or doesn't have, and is non-specific. (meaning it doesn't state how much money the person acutally has / $30, $50, $100, $1000 etc).
Whereas enough refers to the amount of money
needed, in this case to purchase a bicycle and the price of the bicycle is a specific amount.
A specific amount is needed to purchase the bicycle, therefore much is grammatically wrong, because it is non-specific in this context.
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