No, I would not recommend this. You have even summarized why that would be a bad idea.
I eagerly begin to write an answer. That is, until I look take another look at the question and notice it's terribly old. Yet again, I have wasted some precious time..
By this logic you are depriving the site of a valuable answer purely because of the age of the question.
The site isn't here only to help the question asker - we're here to provide a detailed, useful repository for useful questions and answers that will be beneficial to a wide variety of people now and into the future.
It doesn't really matter if the OP doesn't see your answer. Heck, we get people who post a question and never return even on that same day, let alone weeks down the line. That doesn't really matter. If the answer is good then people will vote it up which will help future visitors know that the answer is good, regardless of whether the asker themselves are around to vote.
Also, from a logistical perspective it would be hard to accentuate bumped posts. All posts that get answered / edited are bumped, regardless of whether they were asked 5 minutes ago or 5 years ago. What criteria would you recommend for those that get accentuated and those that don't? The whole point of bumping them is to give them exposure to the wider community. It is a good thing that older posts get bumped because it may bring them into visibility for people who also have answers and didn't know the question had been asked. We don't want to put these people off answering.
The only issue comes with old, crappy forgotten questions getting bumped to the top. Each Stack Exchange site grows and evolves over time so posts that may have been suitable ages ago are no longer appropriate. But if that's the case then people shouldn't be answering them anyway, and a bump will bring their visibility up so people can flag them to close.
Bumping is a good thing for many, many reasons. We don't want to play favourites and potentially put people off answering old questions. That's not in the benefit of the site and community as a whole.