There is no particular idiom 'to get blood in your eye.' But blood in the eye is caused by a burst blood vessel which can happen when you have been crying a lot. So perhaps what Dylan is saying is that he has cried so much over this woman that he has blood in his eyes.

It come's from the drinking phrase "Here's blood in your eye", in this since meaning he is drinking or drunk over seeing her, as to drink in her beauty or literally drinking to get drunk to remember her with nostalgia or get over her, possibly both.

Based on Dylan's song, i think it means desire[sexual desire]. And his lyrics tells about his sexual desire to a prostitute or to his lover, or something. "Gonna get that girl that money that money will buy" "I got blood in my eyes for you, babe I don't care what in the world you do" "I can't wait You got my money, now you're trying to break this date Hey, hey, babe, I got blood in my eyes for you" "I tell you something, tell you the facts You don't want me, give my money back Hey, hey, babe, I got blood in my eyes for you"

The eyes are the windows to a persons soul. So if the window is tainted with blood, that can be saying one or more of many of things. Blood can be associated with love, violence, etc...

"Blood in the eye" means Jealousy! Dylan was saying he doesn't want to let her go... even though he just met her. "The laws of man don't apply when blood gets in a woman's eye" (c) The Black Keys - Ten cent pistol "They wanna get my Gold on the ceiling I ain't blind Just a matter of time Before you steal it It's alright Ain’t no blood in my eye" (c) The Black Keys - Gold on a ceiling