Hi,
I also had progressive myopia. Every time I checked my eyes had gotten worse. My worst prescription was around -6.25 in each eye.
This all changed when I started reading about and practising the Bates Method. As you say, the Bates Method emphasizes the importance of getting rid of the glasses. When Bates stated the fundamental principles of his treatment, the first was that the glasses should be discarded permanently. However, if you read the Better Eyesight magazines you will find references to how Bates was surprised to find that people had been able to be cured, despite the fact that they admitted that they occasionally had been wearing their glasses. So to answer your question: My experience, and that of others, is that it is possible to get improvement even if you wear glasses for such things as driving. However, it slows the improvement quite a bit, so the more time you can spend without them, the better it is.
As for your other question about how long will it take, I think it probably will take a few years without proper guidance - and good Bates teachers (most are unfortunately not very good :-( ) is really hard to get by, so most people are left to figure it out on their own. My best advice is to read Perfect Sight Without Glasses and the Better Eyesight magazines again and again, and not bother so much with other material written about the method. However, if you're going to read more about the method, Stories From the Clinic and Use Your Own Eyes is also good. I do not recommend most of the more modern Bates books. Many of them are written by people with a poor understanding of the method.
As for supplements for improving vision, other people have a lot more knowledge of this than I, so I let other people answer this one.
To make it easier to use your computer without your glasses on, try installing the Swing Windows software. It helps to prevent staring and eyestrain while working with the computer, and it's completely free. You might register the software if you like it for a few dollars, but this is optional. There are also more software on that webpage that might be of interrest to you, like the screensaver, Torch and Bates Quotes.
For more information on the Bates Method, the Imagination Blindness website is a very good starting point.
I hope this could be to some help to you!