The meaning of whose in the bible is the same in modern English.Whose is a Possessive pronoun that Shows ownership or belonging of a noun.
An example of how "whose" is used in the Bible:
Proverbs 16:20 - "Whoever gives thoughtful attention will prosper; whoever trusts in the Lord is happy.
You must keep in mind that Bible's original languages don't have a direct synonymous of (whose) .They use possessive suffixes attached to nouns to indicate ownership