These bundles/Wiis, whatever they are offering all sells out in a matter of minutes everytime. TRU bundles the other day, as you point out, lasted minutes. Actually, they offered them twice, about 30 minutes apart, for a few minutes each time.
Sam's club yesterday had a bundle last 7 minutes.
A few others, such as CC has had bundles in the past day or two that lasted a couple of minutes.
The reason is simple. People, such as me, are running WebMon or something like it. It's a program I found out about from someone else on here a couple of weeks ago. You tell it which web pages to monitor, and you can even specify a specific part of the webpage, such as the "Out of Stock" label, and it lets you know within a minute of any change to that webpage. You just click on its alert and it launches the webpage and you click "Add to Cart" and you have one within a minute of it becoming available. Google Webmon and you can download it from the author's site. I wouldn't download it from just anywhere, as you never know what it might have in it.
Though it sounds simple, it still wasn't easy. I've been running it 24 hours a day, except for my drivetime, for over two weeks and just finally hit Walmart's bundle today. Since the offerings are for such a short time, even just going to lunch, etc. can mean you miss it, and with the demand what it is, the offerings have been few and far between.
It helps, but is not necessary to know a little about html to use Webmon. If you do, you can narrow down what it is watching to decrease false alarms. Good luck if you choose to use it. It did finally score for me, but it took a while.
So, to make a long story short... No, you can't manually compete against people running automated tools to happen to catch a Wii being offered on the Web. You'd have to do nothing but sit and refresh pages constantly for days. People with automated tools will always snatch everything within minutes.