John Gill Commentary 1 Kings 2:19

"Bath-sheba therefore went unto king Solomon, to speak unto him for Adonijah. And the king rose up to meet her, and bowed himself unto her, and sat down on his throne, and caused a throne to be set for the king`s mother; and she sat on his right hand." — 1 Kings 2:19 (ASV)

Bathsheba therefore went to King Solomon, to speak to him
for Adonijah
She went from her own house to the palace; for she might not live at court; or however had an apartment to herself, from where she went to the king with her suit in favour of Adonijah:

and the king rose up to meet her, and bowed himself to her ;
upon her entrance into the presence chamber, in honour to her as a parent, he rose up from his throne, and made his obeisance to her, as a dutiful son:

and sat down on his throne, and caused a seat to be set for the king's
mother ;
a magnificent seat or throne, as the word is, was ordered to be set for her:

and she sat on his right hand ;
where he placed her in honour to her as his mother; so Nero ^F1 placed Tiridates king of Armenia at his right hand, to do him honour.

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FOOTNOTES:

• F1: Suetonius in Vit. Neron. c. 13.