Interesting. My general "rule of thumb" for background (off-peak or MAN) is that it's generally the lowest intensity one can measure. Again, just a "rule of thumb", there are exceptions (holes in the continuum, e.g., Au La in Fe bearing minerals).
Can you share a screenshot of the plot for the Bi La MAN calibration curve with us?
Attached is a PDF of the Bi M-alpha MAN assignment and fit.
The 8 reference materials used in this fit are: Cr2O3 (#2), TiO2 (#5), MgAl2O4 (#13), Cr (#27), Ag (#34), Ti (#45), Sb (#55), and SiC (#133).
The relative-percent-deviation is 1.79, the intercept is -0.0135, and the Z-fraction is the default 0.7.
Also attached is a PDF of wavelength scans (JEOL units, PETJ) from Sandrin Feig's excellent EPMA-Method Development Tool.
The S K-edge should be circa 160.7 mm, and the scans shown include: Bi2Se3, ZnS, and FeS2.
There is a tail from S K-beta1 on its high side, which extends under the Bi M-alpha peak (at about 164.0 mm).
I attribute this tail to the effect of the S K absorption edge.
This S-related tail presumably gives rise to fictive Bi M-alpha intensity, when S is abundant.