Is it possible to dual wield a whip and a longsword?
It's technically allowed as far as I know, but with a penalty of -4/-4 (with Two-weapon fighting) because neither is a light weapon, it doesn't seem very practical.
With Whip Mastery/Improved Whip Mastery and a light weapon (such as a kukri), it can be pretty nice for a warpriest.
Alternately, the scorpion whip is a light weapon that doesn't require a separate proficiency (like bows/composite versions and short sword/gladius). A bard focused on performance combat with gladius/scorpion whip could be an option.