Never encountered this name before, but believe it should be written as ბედისა in Georgian.
-- Anonymous User 9/17/2009
To be a little bit more precise: this name is derived from Georgian ბედი (bedi) meaning "fate" (combined with either a diminutive suffix or a suffix meant to indicate the gender of the name). Also compare Georgian ბედისწერა (bedists'era), which also means "fate".
This can easily be checked in dictionaries or on-line sources such as Wiktionary: