Word that corresponds to "flew" or "drove" when riding a train

While not common or current, train is a verb

[NO OBJECT] DATED Go by train: Charles trained to Chicago with Emily [Oxford Dictionary Online]

American Heritage lists it without the DATED catergorization

To travel by railroad train

You might say, Are you going to fly or train it?

Since AmTrak is the only cross-country passenger rail system in the United States, you could say "She AmTraked from San Francisco to Houston" (assuming that AmTrak serves Houston these days—it didn't when I was a college student looking for alternatives to Greyhound).

You probably don't want trained (which, of course, primarily means "got into athletic or working condition by practicing") or railroaded (which idiomatically can mean "convicted on trumped-up charges"), though either option is available if you don't mind eliciting smiles or quizzical looks before you explain "I mean, she took the train from San Francisco to Houston."

Incidentally, when I was in school and had to use Greyhound buses to get to Houston from Maryland, a common description for that mode of travel was "hopping the dog."

UPDATE: My original answer was intentionally United States–specific because the OP's question asked in particular about how to refer in one word to a train trip from San Francisco to Houston. I believe that the verb Amtraked would be immediately recognizable to most U.S. hearers, but it isn't in common usage, and it certainly isn't comprehensible (or apt) outside the United States.

A much more popular way (in the United States) to describe having traveled by train is "rode the rails." For example, from Edward Hungerford, "America Goes Back to Work," in Harper's Magazine (October 1920):

As far as Garrison we rode the rails of the original main line of the Northern Pacific, and when we passed the marker for the "last spike" I was reminded of the time, away back in the eighties, that the far-seeing Henry Villard had brought the investors of the enterprise out over the ungraded track five days from St. Paul to witness the event, and how they, alarmed by the vast expanse of undeveloped territory, had telegraphed and cabled to sell their holdings, thrusting the road into a financial crisis.

From F.P. Rolf, W.H. Davenport, and P. Bowerman, The Modern Omnibus, (1946) [snippet]:

W. H. Davies, the most "bird-like" of living lyricists, was a cattleman, a berry-picker, a day-laborer, a "super-tramp," until his foot was cut off when he rode the rails in Canada.

From Charles Musser, Before the Nickolodeon: Edwin S. Porter and the Edison Manufacturing Company (1991):

To counter its image as a coal carrier, the Lackawanna Railroad, known as "The Road of Anthracite," developed an advertising campaign in which passenger Phoebe Snow, dressed in white, rode the rails and praised the line's cleanliness in such slogans as: "Says Phoebe Snow, about to go/Upon a trip to Buffalo:/'My gown stays white from morn till night/Upon the Road of Anthracite.'"

And from Wendy Z. Goldman, Women, the State and Revolution: Soviet Family Policy and Social Life, 1917–1936 (1993):

Dreaming of trains and travel, Vasily ran away from home repeatedly only to return, gloomy, silent, refusing to explain where he had been. Like Grisha and Aleksei, he rode the rails to various towns and cities, begging and stealing to survive. He was unhappy both at home and in the children's colony.

A Google Book search for "rode the rails" also turns up such titles as When Beauty Rode the Rails: An Album of Railroad Yesterdays (1962), When Fresno Rode the Rails (1979), When We Rode the Rails (1983), When Eastern Michigan Rode the Rails (1984), and Victory Rode the Rails: The Strategic Place of the Railroads in the Civil War (1992). Part of the appeal of the phrase "rode the rails," I suspect, is that it sounds like a gentle play on the word railroad.

It's worth noting that "riding the rails" is especially associated with hobos who traveled (illegally and for free) by boarding freight trains as they pulled out of train yards after loading or unloading their cars of freight; this act is also known as "hopping a freight." I don't know whether the phrase "riding the rails" is common outside North America.

As for single-word terms for traveling by train, I agree with Erik Kowal that there aren't any truly satisfactory ones in common usage.

There's currently no analogous equivalent to bus(s)ed, flew or flown in everyday use that relates to train travel. The best alternatives I can think of that might normally be employed are travel(l)ed, took, transported, and conveyed. Compare:

1) "She was bussed from San Francisco to Houston"

2) "She flew from San Francisco to Houston"

3) "She was flown from San Francisco to Houston"

4) "She travelled by train from London to Edinburgh"

5) "She took the train from London to Edinburgh"

6) "She was transported by train from London to Edinburgh"

7) "She was conveyed by train from London to Edinburgh"

Of those four alternatives, 4) and 5) are the most idiomatic in British and American English, 6) the least.

Entrain, with senses “(poetic, intransitive) To get into or board a railway train” and “(transitive) To put aboard a railway train” seems a slight possibility. For example:

She entrained at San Francisco for Houston.
She entrained herself at San Francisco for Houston.