How much of a difference does giving blood make to recreational cycling?
If you are riding near your aerobic limit you'll definitely discover that you've lost aerobic capacity during the next 12-24 hours. It can take that long to replace the red blood cells you've lost. 

Since a blood donation is about 10% of your blood capacity, your aerobic capacity will be down by 10%

I wrote the rest of this before I saw your comment that you've given blood many times. I'll leave it in the post for future readers.

Initially, the main issue is blood pressure. Plenty of fluids are recommended as soon as you finish giving blood. It only takes an hour or two to overcome this. 

The conservative advice would be to avoid cycling for the next 24 hours. Until you know how you react to giving blood this is what I recommend. After giving blood a few times you could try riding gently and see what happens. I would still avoid riding on roads in traffic. 

Edit: see also the link provided in the answer by @super.