Since trash bags are used in American homes as a means of garbage
disposal I have been wondering, how much trash in a landfill is
actually the garbage bags we use to throw the trash out?

That's an interesting question. But you can get a rough, intuitive
idea by observing your own garbage bags. An unfilled bag is rather low
in mass & volume compared to when it is filled with refuse. The bags'
contribution to landfills by those parameters is probably less than
1%.

   Their contribution to the *dynamics* of the landfill, on the other
hand, may be very significant. The various materials trapped within
may be subject to very slow decomposition. There may be recognisable
cake leftovers from my 16th birthday in there.