Interesting find - looks like a bug top me.
I have been testing a lot of playlist exports recently, but I never looked closely at the relative path file names in them until just now. What format of playlist are you exporting? I do see the problem with XSPF playlists, but when I export as M3U or PLS, it does use relative paths.
Test exporting as XSPF playlist:
I edited the Library preferences to use relative path, then created a new test playlist, which I then saved with a text editor so it could not change. Then I re-edited the preferences to NOT use relative paths, and modified the play list. After it was automatically exported, I also saved it with a text editor so it could not change. Now when I compare the two files, they are completely identical except for the one new track I added in the second one.
(That one new track proves I am comparing a playlist exported while preferences were set to use relative file paths to the other one exported while that option was not checked.)
Of course, the bigger issue for me is that an exported XSPF playlist should not have any file path in it at all - although that field is valid, it is also optional in the XSPF standard, and including it in an exported file totally defeats the entire purpose of using XSPF. But still, if Music Bee is going to insist on including the file, then it should honor its own preference settings by using relative file paths when called for.