Stumble traffic is very fleeting. What with the lastest panda updates I say away from fast traffic, as this might affect your rankings.
You could add a stumbleupon button to your site, link it to your account and it's as easy as pressing a button.
The answer to your question is in Stumbleupon. If you are using Stumbleupon there is an option to share a website. Just you need to add title and a small description about the website. A word of caution, either your site should be informative to many or should be interesting to make users share it to others. If you try to bookmark your site just for namesake for example say like this is my new website take a look etc, such sites will be deleted from their database immediately.