Carolyn,
 
What you said about a conventional time line and counting spaces between the years is correct, EXCEPT that in this case the the sequence of numbers has been altered. Year 1 B.C. was followed not by the year 0, but by 1 A.D., so you do have to allow for the missing "year 0".
 
For example: The normal mathematics number line logic that you used:
 
-3..........-2..........-1..........0..........1..........2..........3
 
Adding three years to -2 would result in -2 + 3 = 1
 
The actual sequence of years on the calendar:
 
 
-3..........-2..........-1..........1..........2..........3
 
If you used the formula above -2 + 3 = 1 you would now get the wrong answer. You can see that by your method of counting the spaces on the CORRECTED timeline works fine. But to directly add B.C. (negative) years to A.D. (positive years), you do have to add a year as you cross from 1 B.C. to 1 A.D.
 
The problem is not the math, it is that the year 0 was left out in the sequence of years on the calendar system.