In Ḳid. 72b, Adda bar Ahaba, a rabbi of the third century, is said to be "sitting in the bosom of Abraham," which means that he has entered paradise. With this should be compared the statement of R. Levi (Gen. R. xlviii.): "In the world to come Abraham sits at the gate of Gehenna, permitting none to enter who bears the seal of the covenant"--Jewish Encyclopedia, 1906, Abraham's BosomLooking up this reference of Kid 72b, it's found at the very end of the Kiddushin 72b (Gemera) (קידושין עב,ב גמרא) (this is a tractate of the Babylonian Talmud) it reads:
דאגמא איכא בבבל אדא בר אהבה יש בה היום יושב בחיקו של אברהם
"There is a Fort Agama in Babylon wherein dwells Adda b. Ahabah: today he sits in Abraham's lap;"--Kiddushin 72b (Gemera)The word יושב means to "sit" or "dwell," and it frequently used in the Hebrew bible for people settling down or living in an area (as well as just sitting). The phrase that can be translated as "bosom/chest of Abraham" is בחיקו של אברהם , the word של meaning "his", בחיקו (b'heyko) means "in bosom/lap," and with אברהם meaning Abraham.
The word בחיקו 'in the bosom' is used the Hebrew bible twice:
Proverbs 6:27--הֲיַחְתֶּה אִישׁ אֵשׁ בְּחֵיקוֹ; וּבְגָדָיו, לֹא תִשָּׂרַפְנָה
Can a man take fire in his bosom, and his clothes not be burned?--Proverbs 6:27
Exodus 4:6--וַיֹּאמֶר יְהוָה לוֹ עוֹד, הָבֵא-נָא יָדְךָ בְּחֵיקֶךָ, וַיָּבֵא יָדוֹ, בְּחֵיקוֹ; וַיּוֹצִאָהּ, וְהִנֵּה יָדוֹ מְצֹרַעַת כַּשָּׁלֶג
And the LORD said furthermore unto him: 'Put now thy hand into thy bosom.' And he put his hand into his bosom; and when he took it out, behold, his hand was leprous, as white as snow.--Exodus 4:6The word חיקו is found around 34 times in the Hebrew bible, but I use these specific examples to demonstrate it can mean "chest" or "bosom", specifically (Moses did not put his hand in his lap but just to his chest!). I generally do not use the term "bosom" since its weird in modern speech to say a man has a bosom.
The phrase "bosom of Abraham" is used in Jewish literature (at least this one time) and is not unique to the New Testament.