Bloodshot eyes take from a week to 10 days to fully clear up.
Bloodshot eyes usually happen because your eyes are dry and irritated so you should use some moisturizing eye drops to help add moisture to your eyes and prevent future bloodshot eyes.
If the bloodshot eyes is due to a broken blood vessel then the broken blood vessel needs fixed and treated by a doctor first and then it should take 7 to 10 days as well to clear up.
If the bloodshot eyes are caused by a subconjunctival hemorrhage it takes 10 days for the subconjunctival hemorrhage to resolve on it's own and allow the blood to gradually disappear on it's own.
If the bloodshot eyes have not cleared up within 10 to 11 days you should see an eye doctor about it.