Hello,

If the bloodshot eyes just occurred suddenly, this condition could be caused by various factors. Your dog might have scratched his eyes;
a foreign object (irritant) might be trapped under the eyelids;
this might be a symptom of allergies or an eye infection like conjunctivitis; your dog might have high blood pressure; your dog’s eyes might be irritated from riding with his head outside the car window; or your dog might have encountered a skunk (got sprayed in the face--but I'm sure you'd know if that happened or not) or another critter, outside.

Bulldogs and other breeds with flatter noses and slightly protruding eyes, are more prone to eye problems, and you can read about them, here:

http://www.scamperingpaws.com/health/dogeyeproblems.shtml

For the moment, you can flush your dog's eyes with room temperature sterile saline eye solution (no preservatives added), but in order to find the cause and have it treated, a visit to the vet will be necessary. Your dog needs to be evaluated in person, and then the most appropriate treatment will be prescribed.

I hope all will be well with your dog!

Cher