Don't save date as string, first change the column to a Date type or DateTime in your database
Then save
dtpdate.Value.Date
in the database.
when you load data, use parameters and set the parameter values as below
da = new SqlDataAdapter("select * from Booking where date between @date1 and @date2");
da.SelectCommand.Parameters.AddWithValue("@date1",dateTimePicker1.Value.Date);
da.SelectCommand.Parameters.AddWithValue("@date2",dateTimePicker2.Value.Date);