First of all, I absolutly love my Versys. I've owned countless motorcycle and this is the best all around motorcycle there is. I can see why it won motorcycle of the year in 2008.
Now my first problem with the bike. After turning the bike off, every 30 minutes it makes a sound like the fuel pump or fuel injection or something is re-priming. This only lasts for about 5 seconds each time. Sounds a little similar to when you turn the key on and the system "charges" itself.
Odd thing, I tend to agree with the previous posts in that it is likely the tank venting. This can be especially noticeable if you are parking where the sun can hit the tank.
Worst case would be that you have a short that is letting the bike "think" you have turned the ignition on and it truly is pressurising the fuel pump.
A couple things to try:
1) if you hear the bike doing its thing as you described try hitting the kill switch and see if that stops it. If it is a short, and depening on where it lies, this may stop it. But even if it does not stop the symptom it could still be the pump charging.
2) Disconnect the fuel delivery hose to the injectors and see if it pumps out gas when you hear the noise. You will have to disconnect the hose at a point BEFORE it delivers fuel to the injector. Make sure the disconnected hose can spurt the gas into an appropriate container........you know: a gas can, your wife's prize orchids or the feed dish of that dog next door who likes to bark at night.