First, I'll say that I've always been a good employee (from the employer's point of view) and usually they want me to stay, so I'm fairly up front when I want to learn something. If your employer doesn't want to pay for training, they'll probably lose you anyway, but maybe you can make a deal. Usually if they pay for training, you owe them a year to work it off (or you pay it back).
I might present it that way. If you don't feel comfortable, then the next best thing is try to find a DBA job that includes, or could include the DW stuff. You'll likely have to work harder to do your DBA job and learn the DW stuff, but it might be worth it to you.
Schooling is always good to get the basics. I don't learn that way, preferring books and experimenting, but if you like schooling, try to get a class or two and see if you really like it and can understand it. Above all, be honest in interviews that you've gotten schooling, but not practical experience.
I might also suggest you try to convince your current employer there might be value in a DW there.