Who is supposed to sign certifying the mileage at the top section of this bill of sale?

The owner of the vehicle whose name appears on the title.

Bob or Joe could do it, but it should be someone that knows that the odometer reading is correct, like the seller.

The owner and buyer.

The seller. Why do you even want a Bill of Sale? Get the Title!

If you’re asking whose name gets entered at the first blank space, then it certainly won’t be Drayton Williams as he’s buying the car. 

How can he certify that the mileage is correct (to the best of his knowledge)? Is he intending to sue himself if he later discovers he lied?

Common sense applies: only the seller can certify the mileage: if the seller cannot do that then the seller ticks the appropriate box further down. 

The first box is used if the seller believes that the odometer has already passed the maximum it is capable of showing and at some point started to count from zero again.

The second box is for where the seller believes the odometer reading to be incorrect for any other reason. 

To avoid any liabilities, many sellers (especially used car dealers) always tick the second box. 

Seller though it does not really matter. It can't be used in a court of law.  That is the way they got the car.  The odomenter may come out of a car from the junk yard. They do not know and don't have to ask.  What you see is what you get.  It is what it is.

Seller.                

The SELLER  because that's who is legally liable if it isn't factual. 

The person that is selling you the vehicle signs the bill of sale at the bottom you don't have to certify the miles the person that is selling it just writes them in and then signs it at the bottom and on the title

The seller is responsible for the accuracy of the mileage.