When I've done the carmichael field test (which I haven't done in about 6 months...), I did three miles in one direction, recovered, and then did the second 3 miles in the other direction.
There is variation with wind/no wind, and temperature and rain will also mess things up a bit, but the data was good enough for me to check progress.
I'd also recommend riding at a time when the wind is less - for me, that meant early in the morning.
There are two effects that you should be looking for:
1) For a given length time trial, as you get more fit, you should be able to hold a higher average heart rate over the length of the test. When I was starting out last year, I could hold my heart rate in the 165-167 range, but by mid summer, I held 171 for about 5 minutes straight (175-179 is my max).
2) Look at the time it's taking to do the test compared to last time.
I should also note that this isn't something you want to do very often. Time trials are painful, and the 3 mile distance is a particularly painful one. It takes a lot of mental toughness to do it, and it takes a lot out of your body.