Looking through the docs and trying to tests locally, it appears that the basexclient command does not use the USER or PASSWORD fields in .basex when run.
That is, given this in my ~/.basex file:
USER = admin PASSWORD = admin
It should actually do so (I just tried, and it worked for me). Did you possibly have another .basex file located in the directory where you started basexserver from?
Just in case you haven't found this by yourself: [1] describes which directories are checked for .basex files when starting BaseX.
Hope this helps, Christian