Comparing two bitmasks in SQL to see if any of the bits match

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The answer to your question is to use the Bitwise & like this:

SELECT * FROM UserTable WHERE Roles & 6 != 0

The 6 can be exchanged for any combination of your bitfield where you want to check that any user has one or more of those bits. When trying to validate this I usually find it helpful to write this out longhand in binary. Your user table looks like this:

        1   2   4
------------------
Dave    0   1   1
Charlie 0   1   0
Susan   0   0   1   
Nick    1   0   0

Your test (6) is this

        1   2   4
------------------
Test    0   1   1

If we go through each person doing the bitwaise And against the test we get these:

        1   2   4
------------------
Dave    0   1   1   
Test    0   1   1
Result  0   1   1 (6)

Charlie 0   1   0
Test    0   1   1
Result  0   1   0 (2)

Susan   0   0   1
Test    0   1   1
Result  0   0   1 (4)

Nick    1   0   0
Test    0   1   1
Result  0   0   0 (0)

The above should demonstrate that any records where the result is not zero has one or more of the requested flags.

Edit: Here’s the test case should you want to check this

with test (id, username, roles)
AS
(
    SELECT 1,'Dave',6
    UNION SELECT 2,'Charlie',2
    UNION SELECT 3,'Susan',4
    UNION SELECT 4,'Nick',1
)
select * from test where (roles & 6) != 0  // returns dave, charlie & susan

or 

select * from test where (roles & 2) != 0 // returns Dave & Charlie

or

select * from test where (roles & 7) != 0 // returns dave, charlie, susan & nick

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