The necessity of hiding the salt for a hash
The answer here is to ask yourself what you're really trying to protect from? If someone has access to your database, then they have access to the encrypted salts, and they probably have access to your code as well. With all that could they decrypt the encrypted salts? If so then the encryption is pretty much useless anyway. The salt really is there to make it so it isn't possible to form a rainbow table to crack your entire password database in one go if it gets broken into. From that point of view, so long as each salt is unique there is no difference, a brute force attack would be required with your salts or the encrypted salts for each password individually.
Hiding a salt is unnecessary.
A different salt should be used for every hash. In practice, this is easy to achieve by getting 8 or more bytes from cryptographic quality random number generator.
From a previous answer of mine:
Salt helps to thwart pre-computed dictionary attacks.
Suppose an attacker has a list of likely passwords. He can hash each and compare it to the hash of his victim's password, and see if it matches. If the list is large, this could take a long time. He doesn't want spend that much time on his next target, so he records the result in a "dictionary" where a hash points to its corresponding input. If the list of passwords is very, very long, he can use techniques like a Rainbow Table to save some space.
However, suppose his next target salted their password. Even if the attacker knows what the salt is, his precomputed table is worthless—the salt changes the hash resulting from each password. He has to re-hash all of the passwords in his list, affixing the target's salt to the input. Every different salt requires a different dictionary, and if enough salts are used, the attacker won't have room to store dictionaries for them all. Trading space to save time is no longer an option; the attacker must fall back to hashing each password in his list for each target he wants to attack.
So, it's not necessary to keep the salt secret. Ensuring that the attacker doesn't have a pre-computed dictionary corresponding to that particular salt is sufficient.
After thinking about this a bit more, I've realized that fooling yourself into thinking the salt can be hidden is dangerous. It's much better to assume the salt cannot be hidden, and design the system to be safe in spite of that. I provide a more detailed explanation in another answer.
However, recent recommendations from NIST encourage the use of an additional, secret "salt" (I've seen others call this additional secret "pepper"). One additional iteration of the key derivation can be performed using this secret as a salt. Rather than increasing strength against a pre-computed lookup attack, this round protects against password guessing, much like the large number of iterations in a good key derivation function. This secret serves no purpose if stored with the hashed password; it must be managed as a secret, and that could be difficult in a large user database.