Perhaps I am assuming too much, but any sane universal health care system will require you to be a resident of a state for some period of time. Otherwise, then people will just hop a bus as you said and run the state dry.
Assuming that it requires residency, that requires that the sick person quit their job, find a place in the new state to live and work for say a year or two while staying alive with a dire sickness. It's not just a bus ticket that you need to relocate, there are many more significant costs associated with a move.
And even in that case, unless the state is already overcrowded, this is essentially a way to grow the state's residency and thus it's tax base.
