Sounds like you're going too hard on the test.

Maybe you're staring so hard at the numbers that you're forgetting to blink?

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Zen and the Art of Triathlon. Strava Workout Log
Interviews with Chris McCormack, Helle Frederikson, Angela Naeth, and many more.
http://www.zentriathlon.com

No such thing as to hard on a 20 minute power test. You go as hard as you can go while still being able to make it 20 minutes

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Yellowfin Endurance Coaching and Bike Fits
USAT Level 1, USAC Level 3

i get them although not extremely bloodshot. do you have a fan blowing in your face? my fan is about 2 feet away from my face

i also get them when riding for 5-6 hours outside even though i'm wearing sunglasses

do you see brown stripe on your underwear with your red eyes? If yes, you are going to hard. ;)

same here.
i've found its the sweat that gets into my eyes regardless of headband/towel strategies.

Visine is your friend