This is isn't a simple song. Bruce isn't just pining after some girl like some pop song. Consider the context of his life at the time and the message of the whole Tunnel of Love album. I believe that when he says he "ain't got you" that he's talking about his wife at the time. He's got her (she's his wife) but he hasn't really got her, she hasn't fully opened up to him and he's lost his connection with her. Similar to the message in Brilliant Disguise - "Is that you baby, or just a brilliant disguise?". Ain't got you, means that he hasn't truly got her/she's not being completely true to herself when she's with him.
This is isn't a simple song. Bruce isn't just pining after some girl like some pop song. Consider the context of his life at the time and the message of the whole Tunnel of Love album. I believe that when he says he "ain't got you" that he's talking about his wife at the time. He's got her (she's his wife) but he hasn't really got her, she hasn't fully opened up to him and he's lost his connection with her. Similar to the message in Brilliant Disguise - "Is that you baby, or just a brilliant disguise?". Ain't got you, means that he hasn't truly got her/she's not being completely true to herself when she's with him.