Light's note to Yuri is a note written by Light Yagami.
Don't worry, Yuri. It'll be okay. I'm going to look for a chance to grab the guy's arm and pin him down so he can't use the gun. My dad's a detective and he's taught me what to do in emergencies like this. The guy's pretty small and weak-looking. I'm sure I can restrain him.
When held hostage on a bus headed for Spaceland by Kiichiro Osoreda, Light writes this note. He shows the note to his date, Yuri, with the intention of the man sitting behind him (who has been following Light for some time, since he is suspected of being Kira) noticing it. As planned, the man behind Light urges Light not to attack the hijacker. Light then points out that the man has an accent that is clearly not Japanese, and the man admits that he is from America. Light argues that he cannot trust the man as he may be the hijacker's accomplice. Yuri asks Light what he means by this, and Light explains that in hijackings such as this, the hijacker often has an accomplice sitting by.
In order to convince Light that he's not working with Osoreda so that Light won't try and attack the hijacker, the man shows Light his I.D.: an FBI badge reading "Raye Penber". Just as he planned, Light now has the man's name and can kill him with the Death Note.
Penber is worried when he thinks Light drops the note, which Osoreda then picks up, but this is, in fact, another note for a different plan altogether.