Earlier quoted context omitted.
When an app nags me for a review, it really gets in the way and hinders my usage of it. A bad review is a totally legitimate response to that. If this is your only solution to biased reviews, then you have no solution, you just have a way to move the problem around some. If you don't want silly one-star reviews complaining about the prompt, don't interrupt people when they're trying to get something done.
No one said nag. People seem to be be assuming the worst possible behaviour. Asking once with a "Don't ask again" and "Later" option is pretty standard. The original post said a popup is annoying enough to deserve a 1-star review. I strongly disagree and if you enjoy free apps, it's one of the few ways to really thank the developer.
If you only ever ask once, don't you lose out the next time you release a new version and all the reviews get reset? The standard seems to be to ask for every new version, which is a major pain in the behind.
Speaking only for myself, I don't one-star any app just for asking once. I only do it to repeat offenders. I'd prefer never to be asked, but if it's just once, it's easier to just dismiss it and get on with things.