Yes, I happen to have a conscience too. And yes, it can be hard to prove the previous owners knew but it's been done before. As to why you weren't told, perhaps it wasn't required by law at that time? Here in PA, the Disclosure Law will probably take affect this fall. BUT, for a number of years, most knowledgeable folks weren't accepting an Agreement Of Sale w/o a Disclosure Form from the Seller. (We didn't purchase our home W/O one even back in 1994.) If you can find out the make, model, and such of the carpet when you rip it up (there may be a label or somethin' underneath somewhere), then you can find out when the mfgr. made it. And at a worst-case scenario, that will tell you the year(s) it was made and you can calculate if the previous owners were there at that time. Also, how did you know it was asbestos tile/glue? And would it be reasonable for the previous owners to have known like you? If you gather the facts, you can then contact the attorney you used at closing to see if you have a case. (You did have an attorney, right?)
I'd still check anonymously w/your trash hauler as to what their policy is, what size the stuff must be, what day you can put it out on the curb, and in what quantities.
As for removal, again, if the tile is glued to an underlayment such as lauan, then you get a coal-type shovel or an ice chopper underneath, and rip it up VERY CAREFULLY! It has to be glued down onto something smooth. If there's an area that's already loose, and you're DEFINITELY replacing the tile, go ahead and rip up a piece to see what you can see. If you have a basement or crawlspace, perhaps getting underneath will help in determining if what you see on top is the SAME as what you see from underneath. (I can't imagine the time being directly glued to a sub-floor. If it's plywood, see if you can tell how thick it is. Using a wide-bit drill, drilling down a little at a time, will help show the layer(s) under the tile.
E-mail me directly or post up on the Forum. My best to ya and hope this helps.