First, it's very unclear exactly what kind of flooring you have, where
it's located, what is rotted, how it's all held in place, etc. If you
have rotted material, like a sub floor, then just covering it up is not
an option.

I'd also ask the same question as the other poster. Are you sure it
contains asbestos? Has it been tested?

I wouldn't get freaked out by the fact that you were living with
asbestos in floor tile without knowing it. It only becomes dangerous
when it's disturbed and enters the air. And all you did
was chip out some of it, it's unlikely much entered the air. Now, if
you start cutting it up with a saw, that's a diff matter.

I'd check the local laws regarding approved removal methods and who can
do it. Since you are concerned about selling the property, I would
most likely go with removing it completely as opposed to
just covering it up. Generally, the procedure is to seal off the area
that contains it, establish air flow that sucks air out of the area to
the outside and a HEPA filter, wet it down and then remove it in as
large sections as possible, using suitable protection.