Hi funguitar,
Triplets and BIAB's notation of them seems to be mysterious to me. Below are some screen captures to explain what I mean. (The images all refer to exactly the same set of notes with exactly the same swing-based (i.e. triplet-based) style; _CBOOGSL.STY.)
1. The image below is when I have BIAB in
Editable notation mode and I put in some quarter note triplets.

2. I then turned off the
Editable notation mode and went into
Regular notation mode and the notes displayed as the image below shows. (I lost my triplets.)

3. Next I thought I'd try a
print preview of the notes when I'm in
Regular notation mode. This gave me the below results.

4. Lastly, I wondered what a
print preview would look like when I'm in
Editable Notation Mode. The below images says it all.

In summary, it looks like BIAB
does have the ability to display quarter note triplets properly but that there is some glitch that occurs when going from
Editable notation to
Regular notation.
With the above in mind, I'd try setting your music into
Editable notation mode and then seeing if it prints correctly. (I'll send a note to Support and refer them to this thread to see if there is something that can be done to unify the display and printing of triplets.)
Kind regards,
Noel