Rejection isn't a big deal when you're trying to get an apprenticeship, mostly because you already know how difficult it can be to get one. While it can get discouraging, make sure to remember that even if it takes time, you'll get what you want if you keep at it. My best advice would be to really be straightforward with the people you ask. Tell them it's what you really want and ask them what you need to do to prove you are up to the challenge. Let them know that you aren't like everyone else; that you will work hard and do what it takes to become great. If they really don't have the time to offer you an apprenticeship, see if they'll let you do some "free" work around the shop, like sweeping up or something. And in return, they can teach you a technique or two while they are working. I find that if you have the talent and dedication, there are always people who will be willing to give you at least some kind of chance.

If you really can't find anyone to give you a chance, save up for a decent tattoo machine and some fake skin. Have the art professor help you if he's willing to. Practice practice practice. Then, when you start to figure out some techniques on your own, you will have the practice skin tattoos to show in a portfolio as well. I'm sure that I don't have to tell you this, but never practice on a human being. Not only is it dangerous, but if you tell the tattoo artists this, they will see you as reckless and too impatient to learn properly and you'll never get your chance.

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...aint no saint inside this skin...

"I was just thinking about what my life was like before you came here. I never had a need for an emergency transvestite."