The right to travel is a long-established and inalienable right, and rightly so since without it we have no liberty, we are simply prisoners. By establishing public transportation services, the right to travel on them is not excluded.
The Fourth Amendment says that the people should be secure in their persons, houses, etc. from unreasonable search and seizure - that is, searches without probable cause.
So therefore it follows that a person traveling on public transport retains his/her Fourth Amendment rights; and therefore without probable cause no person can be legally searched while getting on a subway or traveling by bus.
If the means of transportation were privately-owned then those private owners would have the right to make searches a condition of using the transportation. But since it is the government which owns the transportation, it is limited in what it may do by the same rules that pertain to all other acts of government.
Yes, I agree with your points, However The issue is probable cause, it isn't that simple. Would you agree, that if the burden of proof has been met that someone is on or is about to board a subway or bus with a bomb, that no searches can be conducted on that conveyance, even thought the evidence is thought to be 99% accurate? We should forget about it and just wait to be blown to pieces?
Give me the document and bag search on this one...