I'm not sure a single map of passenger rail service in the U.S. during that period exists anywhere. Probably your best source would be an "Official Guide of the Railways" (published monthly) for the year and month in which you're interested.I will caution you that the quantity of rail passenger service in the US, even in the mid 1950s, was staggering by present standards. Just as a real quick example, there were:
1)Six trains (at least) each way on three routes between Chicago and Los Angeles
2)Eight trains each way on three routes between Chicago and Minneapolis/St.Paul
3) 17 trains (each way) on three routes between New York and Chicago (this includes the two Erie Railroad trains but does not include the B&O via Washington nor the through sleepers via the Lackawanna and Nickel Plate.
So where do you want to start? You've got quite a research job ahead of you.