No, it doesn't dump or bump a BassResource sponsor. The system we use determines which ad to show - Google OR bassresource sponsor. Never shall the two meet or interfere with each other - ever.
Now, what you're referring to is called "retargeting" in marketing lingo. It's not spyware, malware, or a virus. Simply put, when you visit some websites, then an ad for that site will appear on different sites you visit. And it's not exclusive to Google - all major ad networks work this way. And all major companies do this - Home Depot, ATT, Verizon, Sears, etc. You're probably seeing a lot these days if you did any online shopping during the holidays. Just check out the ads on the sites you normally visit, and you'll see what I mean.
The reason they do this is quite simple, really. You've expressed an interest in their products and services by visiting their site. Perhaps you bought something from them, maybe not. But if they can toss a special offer at you - often exclusive to retargeting campaigns with steep discounts - then you may come back and buy. It's very, very effective.
The more sophisticated companies set cap limits, meaning that if you don't click on the ad within X views, then they stop showing it to you. It seems the ad you're talking about has no such limit. Simply deleting your cookies will fix that, however note that you'll lose all your saved logins as well.
BTW - the "folded" right corner of the ad is a separate link to Google adsense, not meant as an "ad" or "promoting adsense", rather it's informational for YOU in case you have questions regarding the ad network. Some people are very, very suspicious and leery of ads due to the media over-hyping misconceptions and myths about the Internet. The "folded" corner link goes to Google's privacy policy about their ad network. Clicking on the actual ad will take you to that website, often directly to a page explaining the offer details.
Ads are harmless. However, without them, most sites wouldn't exist, including this one. So if you try to block them, you're just hurting the very sites you enjoy.