Suicide: What to do when the person sitting next to you on the train is (possibly) suicidal

I don't usually look at, much less read the screens of the smart phones of those sitting next to me.  Not on trains, buses, or while we're waiting for the light to change.  I don't know why I did today. 

At first, they didn't register.  The woman sitting next to me on the train today was flipping through the pages on her cell phone.  Her finger moving down the screen from top to bottom, she would stop every now and then reading the title of a link to an article.  Or so I assumed.

It was probably at one of these lingering moments as she decided whether to click the link that I noticed the words.  It's amazing what our eyes take in.  There they were:  suicide, and "I want to die."  Not only did my eyes register these words, I was also able to read the full titles of the links.  Each one started with "I want to die." 

Was she contemplating suicide?  Was she a student researching suicide?  How would I know?  What do I do?

She clicked on a link.  The article which I read along with her listed the causes of suicide (i.e. family problems, finances, job-related stress, relationship difficulties).  I see the word "depression."  Her finger keeps dragging the page down, faster and faster it seems and I wonder for a minute whether she's actually reading.

She clicks the back arrow next and we're taken to the previous screen.  I now notice each of the articles above the one she just read are in a lighter purple, the ones below in dark blue.  I know what this means.  All the articles in purple are ones she's read.  Noticing again each article beings with the words "I want to die" I now start to panic.

Maybe panic isn't the right word.  I no longer feel comfortable reading over her shoulder (surely she must have noticed by now) and sit up straight.  I look ahead and decide to dive. 

I take the ear bud out of my left ear and face her.  She looks right at me as if she knew this was coming.
"Are you alright?" I ask.  She nods quickly, smiling.
"Yes."
I'm not content with this answer.  What did I think she was going to say?  Did I expect her to confess she's contemplating suicide?  I could sit back and accept her denial (?) but this feels too simplistic.  Even though she couldn't possibly tell me in a crowded train why she's reading articles about suicide, I decide to ask again.
"The links" and I point to her phone, "you were searching here.  Are you really alright?"
She nods fast.
"Yes."

And, that's as far as I can take it.  I leave my ear bud out in case she wants to say something further.  (If I had plugged myself back into my iPhone I would have been signaling I was done talking.  I assume she figured this out.)  None of this feels good.  Did I overstep?  Should I have kept quiet?  What was I doing reading her phone anyway?  What if she was suicidal and this was her way of asking for help?  And, how pray tell, would I know this?  What was I doing?  

She got off at the next stop (wouldn't you?) and as I sat there in my seat I decided I had no idea whether I did the right thing.  What would you have done?