Do you need a separate bill of sale?
Not required by statute; the county clerk may ask for one
The transfer runs on the notarized assignment on the certificate. If no assigned title can be produced, W.S. § 31-2-105(b) accepts a notarized bill of sale or other evidence of ownership that satisfies the county clerk. Separately, the county clerk may ask for a bill of sale in the format set out in W.S. § 31-2-104(h)(ii). If a bank or other financial institution holds the title on the day of sale, you must give the buyer a signed bill of sale in that format, and the title must follow within 30 days. That bill of sale is signed, not notarized, and certified under penalty of perjury. The buyer may drive on it for 60 days. If the title carries a brand, you must disclose it on WYDOT form MV-602 before the sale and get the buyer's signature. Without that signature the buyer can void the sale.
Source: Wyo. Stat. §§ 31-2-103(a)(ix), 31-2-104, 31-2-105(b), 31-2-109; WYDOT memo, Properly Executed Title / Bill of Sale (22 Sep 2023); WYDOT form MV-602