What does Bella mean?
Directly the Italian/Spanish word bella 'beautiful', from Latin bella/bellus. NOTE: as a given name Bella is most often a short form of Isabella, whose own meaning is 'pledged/devoted to God' (a Hebrew-origin name, NOT beauty); Bella qualifies here only on the strength of the standalone Italian word 'beautiful'.
What does Beatrice mean?
Italian form of Latin Beatrix. Beatrix most likely began as Viatrix ('female voyager, traveler') and was reshaped under the influence of Latin 'beatus' ('blessed, happy'), giving the enduring sense 'she who brings happiness' or 'blessed'.