For example with blowfish it returns something like:
$2a$12$DEzG.CRsHpxpTOAHooQ.wuR6Xe9h6PxFPhOcOvf.lqDNw1TVYVnEO
That contains info about the type of hashing alg and it contains the salt. A lot of resources say to just store this value in the db and it will be secure. But couldn't someone just test a common list of passwords against these values to crack some of them?
The security of password hashing does not come from information being secret. You have already discarded the actual secret, namely the password that is the basis for the hash value. The remaining hash is simply a sort of fingerprint of this original data. The security comes from the fact that it is not possible to derive the original data from the hash. The only possibility is to try all possible passwords and see which produces the same hash. The security here comes from the fact that this is computationally very expensive and unlikely to succeed in a useful amount of time.
The salt is only introduced to prevent somebody from using an already precomputed set of known hashed passwords, forcing an attacker to actually rehash all possible passwords with the unique salt. The salt itself is not secret, neither is the hashing algorithm.
In short: yes, that value is absolutely safe to store in a database.