He can't know that Old Bill was "killed"...
Jack found out what happened after the fact and was able to put two and two together.
The chronology of events is as follows:
- Jack is the captain of the Black Pearl
- Jack knows where to find Cortez' treasure
- Barbossa mutinies and becomes the captain, Jack is marooned
- Barbossa leads the Black Pearl to Cortez' treasure
- Bootstrap Bill feels guilty over what they did to Jack
- The pirates realize they've been cursed
- Bill gives away part of the treasure (to Will) as a way to punish Barbossa and his crew by making it impossible to put all of the treasure back and thus lift the curse
- Barbossa drowns Bill by tying a cannon to his bootstraps
Jack can make a reasonable guess that Bill partook in the share of Cortez' treasure and thus is cursed as well.
Bill would've been stripped of valuables before it happened (scavenging off the dead is common), so any of the cursed coins would've been found and returned to Cortez' treasure, which clearly hasn't happened since the curse is not lifted.
Bill has a family on land. If Bill has a cursed coin and it wasn't on his person when he was being executed, Bill's son (Will) is going to either knowingly own it, unknowingly have stored it with his dad's possessions, or will have known where he spent the coin.
In all of these cases, Will, as Bill's only son, is the best lead anyone has to the missing cursed coin.
The thing is, how did Jack know Turner's blood was necessary to lift the curse knowing that he was marooned by Barbossa before the crew got cursed?
If you're asking how Jack knew that blood of the thieves was required: his knowledge about the curse's existence most likely entails knowing how to lift the curse. Clearly, the other pirates knew as well, so it's not that big of a secret.
If you're asking how Jack could know that the child of a dead pirate suffices, that is unclear. He does know Tia Dalma so he may have enough knowledge of the occult to make an educated guess.
Also keep in mind he is the son of captain Teague, the keeper of the code of the Brethren Court, which can adequately explain how Jack is in the know on general pirate knowledge such as a highly sought after legendary treasure and the story surrounding it.
Or he didn't know for sure but confidently assumed it anyway (it's in character for Jack Sparrow). The rules of magic aren't always scientifically verifiable and you just have to take them at face value.
All pirates (including Barbossa - thinking Elizabeth was Bill's child) seemingly know for a fact that the blood of a dead pirate's child suffices to complete the ritual. How they know it never explained, and shouldn't really be questioned too closely as it's an arbitrary magical rule anyway.