Bridging the gap is a popular idiom derived from Old English. In its earliest use—and not surprisingly—bridge meant “to make a causeway” and gap meant “an opening in a wall.” So, to the drywallers, civil engineers, and road construction crews of the early 14th century (Ha!), bridging a gap was quite literal.
By the early 17th century, the idiom started to take shape as the metaphorical term—that is, the need for an intermediary—we know today. Phrases like stopgap and bridging the gap were adopted to describe problem solving and finding connectivity between two seemingly non-connectable things.