Bae is the popularly used term that is a contraction / dropped letter version of other words, babe and baby. It has been suggested, but never proven, that bae is an acronym for 'before all others.' The actual origin isn't worth debating. Most likely, the term began being used as a texting dropped letter substitute for 'babe' and 'baby' that became both funny and popular to use.
It's usually used in the context of babe or baby, and almost always grammatically incorrect. The term’s usage became popular in 2013 and is still used today.
When words get popular, one of two things tend to happen, they either become synonymous with one very specific thing, or they expand to encompass a wider range of meanings. That latter of which seems to be what's happening today. For sure, it will be used and misused, till something else comes along, so forget about grammatically correct. It's a mad, mad, all-nonsense world out there.
For some sentence examples of how others are using this word follow the link below.