In fact, part of the reason Constantine legalized Christianity was exactly because it was already so popular.
And there was no shortage of heretics before legalization anymore than after.
The earliest notion of a "Bible" in the Christian world was synonymous with "books that are read in the liturgy". (IOW, "the Bible" and "what is read at Mass" were two ways of saying the same thing.)
However, there wasn't unanimity about which books should be read. People in one place read books that people in other places didn't. That's why the canon was taught authoritatively in the West at the end of the 4th C.
There is no evidence to suggest Christianity was popular before Constantine. Even after Constantine the church still faced persecution as Augustine and other of the fathers write. In fact, Augustine talks about how people were so willing to die for Christianity that they went out of their way to be martyred. Augustine had to persuaded them they would be more useful here. It certainly wasn't popular until around 500 AD and like Manfred alluded to, Gnosticism slowly crept in-it wasn't quick as I accidentally implied.
I think there is significant evidence to suggest paganism entered the church after this time. Many of the Roman temples dedicated to Venus were converted to churches for Mary. It's not hard to go back and look at the history of these churches in Rome and the Catholics are rather up front about the matter. It was a small step from worshiping Venus to focusing on Mary. It all happened around the time of Constantine.