The orcs raided Rohan from time to time, and often in the years preceding the
War of the Ring, although they had to be wary of the Rohirrim and other
"unseen powers" that Tolkien says guarded the long stretch of river between
Lothlorien and the Argonath. When Sauron unleashed his forces thousands
upon thousands of orcs crossed the Anduin above the Argonath, enough to attack
both Rohan and Lothlorien. Clearly Sauron's armies were able to cross the
Anduin in force at that time, probably by fording the shallows, but possibly by
creating temporary bridges or using large numbers of boats.
I don't have time to look for the quote you are trying to remember, but I am
sure they didn't say anything about a
bridge.
“I dislike Allegory - the conscious and intentional allegory - yet any attempt to explain the purport of myth or fairytale must use allegorical language. (And, of course, the more 'life' a story has the more readily will it be susceptible of allegorical interpretations: while the better a deliberate allegory is made the more nearly will it be acceptable just as a story.)” (From Tolkien Letter # 131.)