the actual cost of a trip between times square and the national mall is about $200 all things considered based on the ~0.80 federal mileage reimbursement rate for 250 miles. that train corridor is overwhelmingly successful as well so the idea that amtrak isn't a good deal is at odds with reality.
$1 in Jan 2005 is only 1.69 today, not $4 because the velocity of money has decreased dramatically as it has pooled towards the top of the income/wealth spectrum where it doesn't get spent or productively invested.
Inflation is completely possible with no change in money supply. This is handled in economics with the idea of the "velocity of money" which conceptually captures the large range of factors by which prices can increase due to factors beyond money supply, for example an energy price shock or changing consumer and business expectations that result in changes in spending and investment patterns.