Technically, there is no rule stating that you have to suggest an improvement with a comment instead of posting a new answer in the first place, so in that light you could post it as your own answer immediately.
However, as, even if not mandated by a rule, it is commendable to comment an existing answer to suggest an improvement instead of posting the improved version as your own, there probably should be, as suggested by the question, a guideline on how long to wait before answering if the poster doesn't edit their answer in response to the comment.
I think a week, or even a few days if the improvement is very straightforward (easy to verify as correct), should be sufficient. If by then the poster has not edited their answer or responded to the comment in any way, they're probably not very interested in doing so in the future. (If the poster hasn't visited the site during that time, it's better to wait a little longer; perhaps another week.)
You could, of course, ask the poster if it is OK for you to post the improved answer. If they don't respond to that in a couple of days either, just go ahead and post it.
All that said, if the improved version doesn't differ by more than a couple of bytes from the answer, it's probably better just to leave the comment there instead of making a new similar post, even if the answer never gets edited.