We should see here a Hithpa'el Participle, singular feminine, of בקש, preceded by article.
Dictionaries tell, usually under entry בִּקֵּשׁ, that the Hithpa'el of this verb means be asked, be requested.
So, the Participle will mean (female) who/which is asked or (female) who/which is requested. Or, more simple, (female) asked, requested.
Look at ptr PS-t1345