It depends on what causes your bloodshot eye. If your eye is hit by something, the blood vessel in your eye may be popped. In this case, you can treat it with some ice bag, it should go away by itself. If it doesn't work. you should go to see an doctor as soon as possible.
If you bloodshot eye is not serious and you can tolerate it, you can rinse your bloodshot eye with warm water, which can remove irritants in your eye, and it can make your eye moist. After that, dry your eye gently with a clean cloth and drop artificial tears into your eye to keep them moist.