As it happens, I've run into pretty much exactly the same scenario while working on one of my own projects (where a message is encrypted in CBC-mode with a random IV, and the user can either specify a key or a textual password).
Similar questions are discused here and here. To summarize: the purpose of an IV is to ensure that ciphertext remains unique even if the key is reused. As long as you're generating a new IV per message like you said you are, the source of the key doesn't matter as much. Which means you're probably safe reusing the salt as the IV, as far as anyone knows right now. It doesn't even seem like it would even make sense for it to be an issue, because the salt gets put through a cryptographic hash before deriving the key in a different way; as long as you use a good hashing function in PBKDF2 (i.e. SHA-256 as mentioned above), a key so derived is indistinguishable from one which was randomly generated, which in this case it might have been.
However, people uncover unexpected things in the world of cryptanalysis all the time, and straight-up reusing the same data in two places is considered A Bad Thing in principle even if we don't know of any practical problems right this minute. Should you actually be worried about this? At my level of knowledge on cryptanalysis, I'm somewhere between "maybe" and "I don't know," which is a little too much uncertainty for my tastes, so I'm going with the "technically safer" course of action, which is generating separate IV and salt values. Transmitting both the salt and the IV is a perfectly cromulent security practice, and you have nothing to lose if the user directly inputs the key and the salt goes unused.