(יט) לדבר לו על אדוניהו כל דבור שאחריו מלת לו פי' בשבילו, בת שבע חשבה כי זה יהיה לטובת שלמה גם כן, כי בזה ישוב אליו לאהבה בשימלא חשק לבו, וזה שכתוב לדבר לו בשביל טובת שלמה :
To speak to him about Adoniyahu: Every time it says דבור which has the word לו after it, it means on his behalf. Bat Sheva thought that this would be for the good of Shlomo as well, because through this he (Adoniyahu) would return to him in love because he (Shlomo) would fulfill the desire of his heart, and this is what's written "to speak to him for the sake of the good of Shlomo."
You Might As Well Ask For Him to Have the Kingdom: And Shlomo understood he (Adoniyahu) was asking for her as an excuse because it would be forbidden for him to be with her unless he was a king. And if they gave him Avishag it was certain that he would be strengthened in being a king. And Shlomo understood (derived from this) that Evyatar and Yoav were strengthening his hand and advising him as he said "And to Evyatar and to Yoav son of Tzeruyah" If it wasn't for the advice of Evyatar the Kohen and Yoav son of Tzeruyah...(then Adoniyahu wouldn't have asked this).