Yes, there are laws and they differ from jurisdiction to jurisdiction. The only thing that worries me about covering up asbestos is that there are NEW laws coming on the regulation of the stuff.
One of the new laws is the Disclosure Law. If and when you go to sell your house, and you're asked to disclose whether or not the house has asbestos in it, your conscience will affect your answer. If you opt to say NO and the new home buyer can prove that you had to have known about it (what you covered up on the floor), you may be sued for damages. If you opt to say YES, then you have to say where it is and you'll be on the defensive to possibly prove that it's harmless. You all know that asbestos conjures up all kinds of thoughts. And since you own your home, and see it as a non-problem, a prospective home buyer can easily opt-out of buying the home because there's no love-lost no matter what you say about its dangers or non-dangers. They simply can more on to look at the next home.
So, it's a tough call as to whether or not it should be removed or left in place, from the perspectives I mentioned. The material is not a danger unless it's airborn, and with proper masking (which is very inexpensive) and careful removal, I don't see it as an issue. (The jury says the asbestos is in the GLUE; not the flooring itself.) If you're able to rip up the flooring and the underlayment it's been installed on, then, the answer should be easy. As for what to do with it, in MY jurisdication, I can put it in the trash, just a little at a time. In YOUR jurisdiction, just call your trash hauler from a pay phone, work, or someplace else (in case of caller id) to ask of their policy. Since this type of asbestos is non-friable, you may be OK to put it in the trash but you may have to cut it down to size. DON'T, and I repeat DON'T use a power saw!!! This makes the stuff airborn! Put on a mask and use an old chissel to score it and bend it and break it. Or just bend and break it if it's easy enough.
If you need more info, ask away either directly or on the forum. My best to ya and hope this helps.