How hard is a category 2 climb?
For someone who hasn't been riding much, this climb will be brutal. But you'll be surprised at how quickly you'll make progress. Even though you might fail the first time you go up, this ride seems like a great challenge.

Last year I coaxed a friend to start riding again. After a half dozen easier rides, we attempted a mountain climb similar to the ride you're describing. On his first attempt, he only made it about a mile up. On his second attempt, he made it to the top, and on the third attempt, he made it up without weaving all over the road. When you think about it, it's amazing how quickly you can rise to the challenge.

It's probably impossible to adequately prepare on a stationary bike because the feeling of a real climb is different. It will definitely help if your aerobic fitness is already pretty good, but a stationary bike can't really prepare you for the feeling that you're about to start rolling backwards even though you're pushing as hard as you can. :)

By the way, the gearing on your bike will make a big difference. If you can find a bike with a "compact double" or triple crankset, then you'll have an easier low gear available to you, which will make for a more enjoyable ride. A low gear will let you pedal at a faster rate which will avoid wearing out your knees or leg muscles.