0 - None
1 - IDoNotWishToFurnish
2 - HispanicOrLatino
4 - NotHispanicOrLatino
8 - Mexican
16 - PuertoRican
32 - Cuban
64 - OtherHispanicOrLatino

PersonID        Name     Ethnicity   Ethnicity_Name
    1           Joe Smith   26          HispanicOrLatino,Mexican,PuertoRican

CREATE TABLE Application (
   ApplicationID INT,
   EthnicityID INT,
   PRIMARY KEY (ApplicationID, EthnicityID)
);

CREATE TABLE Ethnicity (
   EthnicityID TINYINT,
   EthnicityName VARCHAR(128),
   PRIMARY KEY (EthnicityID)
);

INSERT INTO Ethnicity (EthnicityID, EthnicityName)
VALUES
   (1, 'Asian'),
   (2, 'Hispanic'),
   (4, 'Latino');

DECLARE @InputApplicationID INT = 1;
DECLARE @InputEthnicityIDs INT = 5; --Asian | Latino

INSERT INTO ApplicationEthnicity (ApplicationID, EthnicityID)
SELECT @InputApplicationID,
    E.EthnicityID
FROM Ethnicity AS E
WHERE E.EthnicityID & @InputEthnicityIDs = E.EthnicityID; --bitwise AND operation


SELECT *
FROM ApplicationEthnicity;

DECLARE @QueryApplicationID INT = 1;
SELECT STUFF(
    (Select ', ' + E.EthnicityName AS [text()]
     FROM dbo.ApplicationEthnicity AE
       INNER JOIN dbo.Ethnicity E
          ON AE.EthnicityID = E.EthnicityID
     WHERE AE.ApplicationID = @QueryApplicationID
      FOR XML PATH (''))
   ,1,1,'')