Who coined the phrase "Bema Seat"? I get that "Bema" is the Greek word translated "judgment seat" in the NT. But how did the term "Bema Seat" come to be used? It's a little redundant, like saying "PIN number", but catchy. I'd just like to know how it caught on. Who first said, "We're going to call this not-White-throne judgment the bema-seat judgment"?
Bimah or bema is not only a word in the Greek language.  This is a phrase that was likely borrowed from Hebrew.  בּימה Bema is a platform in Hebrew and is where the Word of G-d, the Torah, is read from.  So it only stands that the NT Scriptures which many argue were composed first in Hebrew or Aramaic, but if that line of thinking is rejected we do know that the writers of the New Testament were Jewish.  Some say the sole exception is Luke, but there are arguments for his being Jewish as well.

So if Bema is Hebrew and means "raised platform" or high place, a term very familiar in the Tenakh, then a seat on that platform where the Word is read or pronounced from would become, of course, the bema seat.


  From Keil and Delitzsch's commentary on Isaiah 53:9, "(Note: The usage
  of the language shows clearly that bâmâh had originally the meaning
  of "height"(e.g., 2Sa 1:19). The primary meaning suggested by
  Böttcher, of locus clausus, septus (from בו ם = מהב , Arab. bhm ),
  cannot be sustained. We still hold that בם is the expanded בא , and
  במה an ascent, steep place, or stair. In the Talmud, bâmâh is
  equivalent to βωμός ,an altar, and בּימה (Syr. bim ) equivalent to the
  βῆμα of the orator and judge; βωμός ,root βα , like the Hebrew
  bâmâh , signifies literally an elevation, and actually occurs in the
  sense of a sepulchral hill, which this never has, not even in Eze
  43:7.)"


So in answer, it is not a term of redundancy but rather a misunderstanding of what the word means vs. what it has come to be understood to represent.

The understanding of the Jewish mindset is not that of a king sitting on a throne like the kings of the Medes and Persians but rather as in  


  John 12:48 KJV, "He that rejecteth me, and receiveth not my words, hath
  one that judgeth him: the word that I have spoken, the same shall
  judge him in the last day."


The Word was read from the Bema, a seat can also mean a place of position or power.  The seat of power/government  This idea and understanding of judgement fits in line with the understanding of Judaism that the books of life will be read and judgement pronounced by the ultimate Judge of the Quick and Dead.
Where would be the place the Judge would read from the Book?  The Bema, of course.
Getting back to the mindset in which these Scriptures were written helps one to more easily understand how phrases came about because they were intimately tied to the culture and contained within the Word.