That’s going to be a tough one to achieve in a formula field because Airtable doesn’t provide any sort of iterator functions for the formula field, where you could step one-by-one through the linked records and check them against another field.
If you are using, or are planning to use a “Pro” subscription, this could definitely be done with the Scripting Block – I’d suggest exploring that route.
What do you mean by “native”? Technically, the Scripting Block is “native” - it is a tool built by Airtable that is baked into the product, and can be used for complex manipulation of records like you are wanting to do.
How about you check the Tasks table? There should be 2 fields that are linked back to the Buckets and Persona tables. So if Task 100 is in Bucket 01 and Persona 02, they will be both present side by side.
another option would be to have a staging table where you have the primary field be a formula between the Persona and the Bucket for example?
I really dont know what you are trying to achieve with this so I can’t help you much.
But of course, @Jeremy_Oglesby suggestion for using the Script Block (which is free till September 2020) would help you a long way. We have many great community members that are offering their services in scripting for a very reasonable price.