Do you need a separate bill of sale?
Not for the transfer — but it can do the reporting
The properly assigned certificate of title is what transfers the vehicle. Missouri's Bill of Sale, Form 1957, is one of the two ways to satisfy the 30-day reporting duty, so it is worth using even though the sale does not depend on it. What you MUST hand the buyer is the assigned title, plus a safety inspection certificate less than 60 days old unless the vehicle is within ten years of its model year and under 150,000 miles. If you live in St. Louis City or Jefferson, St. Charles or St. Louis County, add an emissions inspection under 60 days old. Selling as-is does not remove the inspection duty.
Source: Missouri DOR, Selling a Vehicle; RSMo 307.350.1, 307.380.1