Might have gotten this terribly wrong, but I think I've done this correctly. I took a Youtube video of somebody SRing for a shiny starter in White (this one, if you're curious) and got a clip starting at the time he soft reset and ending at the time the Pokemon hits the ground, when you send it into battle. (Which is the first instance you're able to tell if a starter is shiny in Black and White. Not sure about other games.) From start to end, it was about 1 minute and 11 seconds, or about 77 seconds. Assuming that a shiny Pokemon is obtained on the 8192nd reset, statistically, it'd take about 630,784 seconds, which is about 175 hours and 13 minutes. That's 7.3 days.
Keep in mind that that's statistically how long it would take. It's unlikely that you'll get a shiny on the 8192nd reset, as well as take exactly 1 minute and 11 seconds to go from resetting to throwing out your Pokemon. If it took only one second longer, a minute and 12 seconds, it'd take about 2.3 hours longer.