Your credit score may go down during your first month of reporting.
Whenever you open a new tradeline on your credit report, your score will most likely decrease until the first one or two payments have been reported on that tradeline. This is normal as you are changing the age of your accounts. Most people's score rebounds after a few months of reporting on your new tradeline.
Everyone's credit report is different and affected by many variables. Rent and bills reporting builds history into your credit file without adding debt. Regular payments demonstrate responsibility which the scoring models take into account when determining scores.
Remember, credit is all about demonstrating history. So, typically, the longer you have a tradeline on your credit report, the better.