Bob lives in the United States. Bob didn't pay for a bill, and the bill was sent to a third-party debt collector. When will it start affecting Bob's credit score? For example, will Bob's credit score be affected even if the debt collector hasn't contacted any credit bureau yet?
Credit scores change when something good or bad happens to your file. Companies that extend you credit by issuing you a credit card or loan, report the presence of your account to the credit bureau. Once the credit bureau knows the account exists they can use it in their calculations.
Other bills only get reported when the debt goes to collections. There is no way the credit bureaus could contact every collection agency about everybody in their credit files to see if they have an amount in collections.
How long does it take for a collections agency to report it? No idea. But I wouldn't count on them being slow.