The apocryphal Targum Sheni contains more details of the encounter between Solomon and Sheba.
Here is the short Biblical passage that tells of the meeting between Solomon and Sheba:
1 Kings 10:1-13
10:1 And when the queen of Sheba heard of the fame of Solomon concerning the name of the LORD, she came to prove him with hard questions.
10:2 And she came to Jerusalem with a very great train, with camels that bare spices, and very much gold, and precious stones: and when she was come to Solomon, she communed with him of all that was in her heart.
10:3 And Solomon told her all her questions: there was not any thing hid from the king, which he told her not.
10:4 And when the queen of Sheba had seen all Solomon's wisdom, and the house that he had built,
10:5 And the meat of his table, and the sitting of his servants, and the attendance of his ministers, and their apparel, and his cupbearers, and his ascent by which he went up unto the house of the LORD; there was no more spirit in her.
10:6 And she said to the king, It was a true report that I heard in mine own land of thy acts and of thy wisdom.
10:7 Howbeit I believed not the words, until I came, and mine eyes had seen it: and, behold, the half was not told me: thy wisdom and prosperity exceedeth the fame which I heard.
10:8 Happy are thy men, happy are these thy servants, which stand continually before thee, and that hear thy wisdom.
10:9 Blessed be the LORD thy God, which delighted in thee, to set thee on the throne of Israel: because the LORD loved Israel for ever, therefore made he thee king, to do judgment and justice.
10:10 And she gave the king an hundred and twenty talents of gold, and of spices very great store, and precious stones: there came no more such abundance of spices as these which the queen of Sheba gave to king Solomon.
10:11 And the navy also of Hiram, that brought gold from Ophir, brought in from Ophir great plenty of almug trees, and precious stones.
10:12 And the king made of the almug trees pillars for the house of the LORD, and for the king's house, harps also and psalteries for singers: there came no such almug trees, nor were seen unto this day.
10:13 And king Solomon gave unto the queen of Sheba all her desire, whatsoever she asked, beside that which Solomon gave her of his royal bounty. So she turned and went to her own country, she and her servants.