The 'two earlier songs' that Bruce referred to were 'The dying Young-man and the obdurate Maid' (c.1655-1663/4), and 'The Ruined Lovers' (1663-74). His transcriptions of both can be seen at http://www.csufresno.edu/folklore/Olson/SONGTXT2.HTM#RUNDLVR. Bruce suspected that 'Barbara Allen' was based on the former, but the scenario was hardly uncommon.

The rose-and-briar episode doesn't occur in surviving early examples of 'Barbara Allen', and was presumably borrowed later on from one of a number of different songs that use it. 'Fair Margaret's Misfortune' (Douce Ballads 1(72a), dated c. 1720, though Child thought 'end of the 17th century': see link above) would be one possibility.