As a Christian, I tend to define morality based on the Bible. Can this same gauge be used for societies? How can I apply this metric to societies that are undeniably non-Christian?
In almost all societies, it can't. Perhaps the only societies where this can be used is those where by definition those societies genuinely use the Bible as their moral compass, for example in a monastery.
In most other scenarios, perhaps it is more meaningful to look at the law (in comparison to international / humane law), and how that law is applied (for example: is the application of the law itself horribly corrupt). Now, law (and it's application) vs morality are slightly different topics, but it is perhaps the best indicator we have. You can of course look beyond that into the zeitgeist of the population, but that is much harder to measure accurately.
Coming back to the Bible in the context of morality; the point I would make here is that in many cases, a significant portion of both the in-group and out-group do not accept the morality of the Bible; the most obvious glaring holes here would be things like the Bible's aggressive stance on homosexuality and gender issues (I know that record is old, but they are important). I know very many Christians who have absolutely no issue with homosexuality, and know of others that are fire-brand against homosexuality. To me this simply proves: if different people in the in-group can't agree which way that moral-compass points, then that moral-compass is broken.
To borrow from another answer:
In most modern day societies, morals are basically the same as in the Bible.
Again, I would turn this around: In most modern day societies, the Bible happens to be (give-or-take) basically the same as those in the society. One does not need the Bible to know that stealing and murder is a bad thing, for example.