All of the sentences are correct. "Can I take you home." sounds like an offer to a child or a sick person -- someone who is unable to get home on their own. It implies "can I take you to your home". "Can I drive you home" is similar to "can I take you home", but it sounds a little bit less like it is spoken to a child. "Can I bring you home" sounds a little bit odd. It implies "Can I bring you to my home." But it sounds sort of like you are talking to an object, or a very intimate friend. I think you should avoid saying this sentence. It might get you in trouble.

You don't say "to home" in your examples. There is a rule about this. Can I take you home? Can I drive you home? Can I bring you home? I think the differences are very obvious here.