Searching the e-text at ae-lib.org.ua (1954-5 editions):
I don't find a single mention of "the Barad-Dûr", (or any simplified form thereof), and
I find only two examples of "the Bag End", one of which is "the Bag End garden".
The other is in a quote representing the gossip around Hobbiton: 'hiding up in the Bag End'.
Possibly the audiobook reader added the definite article to Barad-Dûr by mistake, and it wasn't picked up in review.
Bag End can be taken for a play on Cul-de-Sac (French, meaning bum of the bag).
Regardless of whether the lane servicing Bag End existed before the construction of the smial by Bungo and Belladonna, the property at the end of a lane is likely to have been described as "At the bag end" which through the time of construction could be shortened to "The bag end" and then finally "Bag End" be accepted as a formal name (with the play on the Baggins name). Use of "the Bag End" in the vernacular of Hobbiton could be vestigial, representing the speech of the locals at the time of construction a mere 112 years earlier.
Regarding "the Strider", it seems to be the only usage in the whole work, but it may also be the same kind of thing, where the folk of Bree originally referred to Aragorn as "the Strider" which then, over half a century or so, gets worn down to simply "Strider". Gandalf, may have fallen back on an older usage.
