The Bootstrap Paradox is a theoretical paradox of time travel that occurs when an object or piece of information sent back in time becomes trapped within an infinite cause-effect loop in which the item no longer has a discernible point of origin, and is said to be “uncaused” or “self-created”. It is also known as an Ontological Paradox, in reference to ontology, a branch of metaphysics dealing with the study of being and existence. (Source)
Can the time machine be a necessary component of the bootstrap paradox? sure! A really good example is, IMO, the machine in the movie Primer (2004). Does your scenario describe a viable bootstrap paradox? Maybe.
All bootstrap paradoxes focusing on an object have one basic problem: the object never seems to get old. This is because the explanation of the paradox is, IMO, inadequate. Note that the quote above states, "...trapped within an infinite cause-effect loop..." This is NOT a requirement for a bootstrap paradox. In fact, it's almost never the case than an infinite loop exists (at least I've never heard of one where it had to exist, or could even be assumed to exist).
Why? Let's look at your scenario. you-before-first-use finds the machine and uses it, causing you to become future-you. Future-you travels back in time to place the machine. And there's the problem. Future-you watches you-before-first-use use the machine ... and then lives out the rest of his/her life in comfort and profit (having sold the rights to your autobiography). The loop only occurs once. The only way it could occur an infinite number of times is for future-you to always be the one who uses the machine the first time.
Curiously, neither example used in the source I quote above represents an infinite loop, even though the article believes they do. In Heinlein’s short story “All You Zombies” (1959), the protagonist travels back in time to impregnate his/her former self, becoming his/her own parent. OK, the person who traveled back in time didn't disappear. The linearity of time for the traveler is unique with a single loop. It can only be thought of as happening over-and-over if you ignore the future of that aspect of the protagonist (who most likely lived a long and happy life...)
The example of Somewhere in Time (1980) involves a pocket watch. But, once again, the loop only can occur once unless you assume that when Christopher Reeves traveled back in time he somehow merged with his future self.
It's easier to answer the question by asserting a single loop — but then you wouldn't have a question.
Since the loop can only occur once in your scenario, there's no issue with the iron components becoming rusted and failing.
What would it take to get infinite loops in my scenario?
Star Trek the Next Generation investigated two possible ways.
One is like in Star Trek the Next Generation's Cause and Effect. The ship itself is thrown back in time to a starting point. When tracking the linear history of the ship, there is only one ship repeating the same loop in time over and over and over. The show creatively lets the crew in on the secret by providing means of "communicating" outside the loop. There are never, for example, two Picards. There's only ever one. In this case, nothing can age, and so your iron components would never fail. Said another way, time simply "resets" to the beginning of the loop.
The second is STNG's episode Time Squared. In this, a future Picard is thrown back into the past. But this episode cheats the question by never portraying an infinite loop. This is a good example because it shows what to do with the duplicates (Picard and the shuttle craft): they're destroyed in the explosion. So, although the episode does not show an infinite loop, one could be created if Picard took the same actions over and over.
But in your case, you-before-first-use always uses the machine. There's no way to create an infinite loop because you need future-you to always make the choice.
Which returns us to the above stated conclusion: your machine will never take more than one iteration and therefore the component will never wear out. If you figure out how to make iterations, it will either always result in a new machine or in the machine never aging.