Is it correct to return the greeting of "peace" with the phrase: "Wa alaykum bil-salam" (and upon you with peace) by adding the letter baa (بـ), and is there any origin for this in the Sunnah?

Initiating the greeting (salām) is a Sunnah, and returning it is an obligation by scholarly consensus (ijmāʿ). The best form of response is "Wa ʿalaykumus-salāmu wa raḥmatullāhi wa barakātuh" (And upon you be peace and the mercy of Allah and His blessings), by fronting the predicate and using the conjunction "wa" (and). The addition [of "wa raḥmatullāhi wa barakātuh"] becomes obligatory if the Muslim says "As-salāmu ʿalaykum wa raḥmatullāhi wa barakātuh," or it is recommended if he confines himself to "As-salāmu ʿalaykum." As for the phrase "ʿAlaykum bis-salām" (Upon you be peace), it has no basis in the Sunnah, and the greeting is not returned by it.