Betsy is an angelic-faced do-gooder who works for Charles Palantine's presidential campaign. At NYC campaign headquarters, we see her goofing around with another employee, Tom, and they share some pleasant and amusing conversations—maybe a little flirtatious. To our eyes, she doesn't seem unhappy or lonely at all.
Travis Bickle has a different opinion on Betsy. He's been watching her from his taxi, lingering on her, and devouring her image. He imagines she's a beautiful angel who will save him from this festering hell-hole.
Travis eventually gets up the guts to go in and talk to her, offering to volunteer for her campaign and opening with a fairly personal and risky speech, asking her to get something to eat with him:
"I think you're a lonely person. I drive by this place a lot and I see you here. I see a lot of people around you. And I see all these phones and all this stuff on your desk. It means nothing. Then when I came inside and I met you, I saw in your eyes and I saw the way you carried yourself that you're not a happy person. And I think you need something. And if you want to call it a friend, you can call it a friend."
This is the kind of speech that sounds too good to be true… because it is. Travis sounds perceptive, but he's actually just stating facts that are applicable to all humans: We're all a little lonely sometimes, and we're all a little unhappy sometimes, and we all definitely need buddies. However, Betsy thinks for a moment that Travis maybe, just maybe, can see into her soul… so she decides to get a snack with him.
"Yo, Just Give Me a Fruit Salad, I Ain't Too Hungry" – Prince
As they get something to eat—with Betsy ordering a fruit salad and Travis ordering a piece of apple pie with a slice of kind-of-nasty melted yellow cheese on it—Betsy reflects on her initial impression of Travis:
BETSY: You know what you remind me of?
BETSY: That song by Kris Kristofferson.
TRAVIS: Who's that?
BETSY: A songwriter. "He's a prophet... he's a prophet and a pusher, partly truth, partly fiction. A walking contradiction."
TRAVIS: You sayin' that about me?
BETSY: Who else would I be talkin' about?
TRAVIS: I'm no pusher. I never have pushed.
BETSY: No, no. Just the part about the contradictions. You are that.
Maybe this "prophet and a pusher" stuff is partly Betsy's own projection on him: The same way Travis sees Betsy as a pure angel, she sees him as some sort of streetwise prophet dude. (If Travis is a prophet, he's a vengeful prophet— a prophet of destruction). She doesn't sense the vast reservoirs of anger and discontent swirling underneath Travis' exterior—she also doesn't realize quite how maladjusted he is, how peculiar his notions are.
She Would've Preferred a Fun Evening at Dave and Buster's
She agrees to meet up with him a second time, going to a movie with him. Unfortunately, Travis takes her to the same kind of movie he watches all the time—a porno movie. Betsy knows it's a porn movie right away, but Travis insists it's a normal movie. She goes in with him (trust yourself, girl!) and then walks out when it becomes clear it's porn. She tells him, "Taking me to a place like this is about as exciting to me as saying, "Let's f***." Travis and Betsy have both misread each other—Betsy is a person, not an otherworldly being, and Travis isn't a prophet: He's a sad, screwed-up guy.
Once Betsy—still justifiably put off by the porno movie—decisively rejects Travis over the phone, he busts into campaign headquarters and yells at her, screaming that she's "Just like the rest of them!" He leaves without getting violent, but its still a super-disturbing experience. As he descends into insanity, Travis starts plotting to murder Charles Palantine—possibly because Betsy works for him.
Betsy is unaware of this whole plot, and at the end of the movie, after Travis has committed his "heroic" rampage, she actually seeks out a ride from him in his cab. It seems like he's ready to let bygones be bygones, and he insists on giving her a free ride. It seems that Betsy has bought into the heroic myth that's developed around Travis, and it also seems like they're probably not going to have a future together. (Bullet dodged, Betsy.)
By the movie's end, it doesn't seem like either of them ever managed to connect with each other on a real level—although maybe Travis understands that Betsy's a person rather than an actual angel, which would explain his gracious behavior in the final scene. Maybe Betsy understands that he needs help too, that he was and still probably is mentally ill… but their futures are both open to doubt.