Here's how I might do this. I suspect the first day of the week could be identified simpler than I have here.
DECLARE @RUNDATE DATETIME = GETDATE()

-- Set the @@DATEFIRST setting to 1, and capture it so we can restore it back afterwards.
DECLARE @PREVDATEFIRST INT = @@DATEFIRST;
SET DATEFIRST 1 ;

SELECT [BUILD DAY]
  -- Find out what the current weekday is, remove that many days (minus 1, as the first day of the week is day 1) from the date, then add 7 to get when next week starts. Add 14 to find when the week after starts.
  , DATEADD(DAY, 7, CAST(DATEADD(DAY, - (DATEPART(WEEKDAY, @RUNDATE) - 1), @RUNDATE) AS DATE)) AS STARTOFNEXTWEEK
  , DATEADD(DAY, 14, CAST(DATEADD(DAY, - (DATEPART(WEEKDAY, @RUNDATE) - 1), @RUNDATE) AS DATE)) AS ENDOFNEXTWEEK
FROM TESTBUILDS
WHERE TESTBUILDS.[BUILD DAY] >= DATEADD(DAY, 7, CAST(DATEADD(DAY, - (DATEPART(WEEKDAY, @RUNDATE) - 1), @RUNDATE) AS DATE))
  AND TESTBUILDS.[BUILD DAY] < DATEADD(DAY, 14, CAST(DATEADD(DAY, - (DATEPART(WEEKDAY, @RUNDATE) - 1), @RUNDATE) AS DATE))

SET DATEFIRST @PREVDATEFIRST;