All files ending with a suffix without using negation

I am trying to match all files except those ending in .bmp.

Due to some restrictions, I cannot use negation (?:,! :) and links (\ 1, ...).

I made an expression and it works for most lines:

^\w+\.([^b].*|b|b[^m].*|bm|bm[^p].*|bmp.+)$

It matches everything that doesn't end with .bmp - including test.txt, test.bmp.txt, etc. But dishonestly, it allows test.bi.bmp.

Any idea on how to improve the regex so that it matches files not ending in .bmp?