You probably went into shock.
A pint of blood is roughly 500 mL. The "average" adult human can lose 750 mL before going into shock. And well, noone is an average human... so if you're a smallish female, it's quite possible for a blood donation to be a bit more than your body wants to deal with. Yes, you can keep going into shock after you've lost blood.

What I'd do (until you stop feeling icky when exercising) is bring a cell phone with when you ride, and let someone know when you leave and where you're headed. Bringing a light jacket, some electrolyte replacement drink, and a snack isn't a bad idea either, even if you don't normally need those things. Standard first aid for donating blood is "eat something" and "drink something". And wrapping someone who is shocky in a blanket is an easy way to help them. Blankets don't work so well on a bike, so a jacket makes a good substitute.