First of all, never use synonyms just for the sake of using synonyms. Use the precise word that communicates your meaning — this will depend not just on your meaning, but on the context (which may change from one sentence to the next).
It’s probable that none of those three synonyms would be useful to you. “Bachelorette” is only used in specific contexts (mainly "reality" TV). “Lass” is mainly used in Scotland. “Maiden” is old-fashioned. How old is the girl in question? Also, are you using “girl” mainly to indicate her age (in contrast to “woman”), or her gender (in contrast to “boy”)?