My guess would be that the DBD::mysql shared object file (XS part of the module) is linked against the MySql client libs (i.e. another shared lib), which might not be found in the Apache environment. Try setting an appropriate LD_LIBRARY_PATH...

P.S. you're most likely not interested in the .bs file (see Re: Empty perl *.bs files), but rather the .so file, which should reside in the same directory — do an ldd on that .so file in order to see which other libs it depends on...