The Arabic feminine name "Baheejah", "Bahija", or "Bahijah" means "joy". The Arabic feminine name "Baseemah", "Basimah", "Basma", or "Basmat" means "smiling".
"Baseemah" is a feminine form of the Arabic masculine name "Bassam", which literally means: "he who smiles a lot".
Here's a 'net reference to the meaning of the masculine name "Bassam":
http://www.geocities.com/Area51/Lair/1729/arabicnames.txt
-- Nanaea