Something like this might work
SELECT
count(1)
,DATEADD(MINUTE,(DATEPART(MINUTE, date_recordedcl_StartDate) / 15)*15,(DATEADD(HOUR, DATEDIFF(HOUR, 0, date_recordedcl_StartDate), 0)))
FROM raw_bulbstbl_Calls
WHERE
cl_StartTime BETWEEN @StartDate AND @EndDate
GROUP BY
DATEADD(MINUTE,(DATEPART(MINUTE, date_recordedcl_StartDate) / 15)*15,(DATEADD(HOUR, DATEDIFF(HOUR, 0, date_recordedcl_StartDate), 0)))
To get the quarter this will give you a value of 0-3. Multiply by 15 to get 0,15,30,45.
DATEPART(MINUTE, date_recorded) / 15
To round down cl_StartTime to a full hour.
DATEADD(HOUR, DATEDIFF(HOUR, 0, date_recorded), 0)
Then you just add it together like in the query to get the correct timestamp and group by that.