SELECT u_access FROM bookings, users
    WHERE b_rid=$room
    AND b_date='$theDate'
    AND b_uid=u_id
    AND b_id IN
       (SELECT b_id
        FROM bookings
        WHERE b_id IN
               (SELECT b_id FROM bookings
                WHERE '$from' BETWEEN b_time_from AND b_time_till
                OR '$till' BETWEEN b_time_from AND b_time_till
               )
        OR b_id IN
               (SELECT b_id FROM bookings
                WHERE '$from' BETWEEN b_time_from AND b_time_till
                AND '$till' BETWEEN b_time_from AND b_time_till
               )

       OR b_id IN (SELECT b_id FROM bookings
                WHERE b_time_from BETWEEN '$from' AND '$till'
                AND b_time_till BETWEEN '$from' AND '$till'
               )
       )

you're basically searching for any booking which has a start before the period you specify ends, and an end AFTER the period you specify begins... therefore

b_time_till > $from AND b_time_from < $till 

does the same thing as all 3 of your sub-selects

SELECT u_access FROM bookings, users WHERE b_rid=$room AND b_uid=u_id AND (b_time_till > '$from' AND b_time_from < '$till') AND b_id IN (SELECT b_id FROM bookings WHERE b_date='$theDate')