Apprenticeship Question...

Just lookin for some advice. I would love to get an apprenticeship. Before I hit the streets and start tryin to get someone to take me under their wing here is my dilemma. Being that I am 33 years old and I own my own business with also another business part time. I have the dedication it takes to follow through with what I want to accomplish. From what I have been reading it could take anywhere from 3 to 5 years to complete the apprenticeship. It seems that this is a very touchy subject with tattoo artist and I just want to know if this is something that could be accomplished on a part time basis. It does not matter to me how long it takes me to accomplish but I did not want to disrespect any particular artist by asking to teach me under my conditions. It would be hard for me to be in a shop on a full time basis due to my business. Could I spend just a few hours a week under someone to learn this art (doesn't matter if it takes 10 years to me). I am an artist my self and I know what I am capable of , just not sure about the whole time issue and did not want to ask for something that was way off the wall. I guess I just wanted to know what I should expect from asking a professional this. Hope that this was clear and not confusing.