What Simchah does David want to hear?
Rashi: Pardon of the sin. Radak - when a Navi will tell me that You pardoned, it will be Simchah of my Nefesh, which is pained and mourning over the sin. Even though Nasan told him "Gam Hashem He'evir Chatascha Lo Samus" (Shmuel II, 12:13), He promised him only that he will not die, but not that other bodily punishment will not come. Nasan already told him "Lo Sasur Cherev mi'Beisecha", "Hineni Mekim Alecha Ra'ah mi'Beisecha" (ibid., 10-11). David did not pray about them, for it was proper to receive them to atone for his sin; he cannot have Kaparah without them.
Malbim: It is as if the Nega destroyed the build of the body, and now it will be rebuilt afresh. This corresponds to "Techate'eni v'Ezov v'Etaher" (verse 9). Amidst Tzara'as, he dwelled outside the camp and his clothes were torn; this is the opposite of Sason, i.e. external signs that show Simchah. Also, he calls "Tamei Tamei", the opposite of Simchah in the heart. Now, he will have revealed Sason and Simchah in the heart.
Why did Hashem crush his bones?
Rashi: This was when He was angry at him.
Radak #1: "Atzamos" are the body, like "Shemu'ah Tovah Tedashen Atzem" (Mishlei 15:30).
Radak #2: David was confounded due to fear of the punishment, and his bones were crushed.
Malbim: They were crushed via the pain and Nega.
How will his bones rejoice?
Malbim: This corresponds to "Techabeseni" (verse 9), removal of the pain and Nega. There will be sudden joy through the cure.