I find it's not worth a couple of bucks to find out. I have been rejected going only a little below the suggested price. And with rental cars, you can't change anything but size to rebid so you never know what would win. I find the prices change frequently and the suggested prices are pretty good anyway - and they change too.
You can bid the next day. But if it's time-sensitive, you're right, it's not worth the couple of bucks to reject their offer.
But the second tip would seem to work for even the time-sensitive traveller -- even if you wanted to follow their "advice." Has anyone ever had a bid rejected that was supposedly a "good chance"?