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Trinity tells Neo (via his computer) to
"Follow the White Rabbit"
A few minutes later, Neo is invited to a club and although he initially refuses, he changes his mind when he sees that one of the would-be clubbers has a white rabbit tattoo.
How could Trinity have known that Neo would see this tattoo?
It's not like Trinity made a prophecy that would take years to be confirmed.
As she was talking via chat with Neo, she knew that a person with a White Rabbit Tattoo was headed towards Neo's appartment.
I can see two in-universe sources for this information :
It's not that different from the scene where Morpheus sends a phone to Neo, calls him right as he opens the envelop, only to tell him that the Matrix' agents are coming his way.
So, Trinity clearly saw the tattoo coming.
Also, it's not a hidden tattoo. People with tattoos wear them with pride. Maybe not all of them, but Dujour's outfit is clearly designed to show her tattoo off.
Furthermore, if Trinity says something as curious as "Follow the White Rabbit" to Neo, he will be actively seeking every form a White Rabbit can take, because he is eager to meet with Morpheus. Which make Trinity's statement a [TVTROPE] self-fulfilling prophecy.
Now these are not decisive proofs, but add them together and you have a highly probable event.
I don't think Trinity knew Neo would see the tattoo, but she knew there was a good chance he'd see it. On his computer, Trinity typed:
Follow the white rabbit.
Knock, knock, Neo.
Neo hears the knock on his door immediately after Trinity told him about the white rabbit and the knock. Trinity connected the white rabbit with the door knock in Neo's mind and made it more likely he'd notice it.
Dujour's clothing is revealing enough that the tattoo is always visible, even when she's just standing next to Choi. We can still see it (barely) in a different shot during the scene (taken from this Youtube video):
The tattoo would be even more obvious without the shadow and if the camera was focused on Dujour instead of Neo. Trinity knew the tattoo was highly visible because she and other Matrix hackers can see into the Matrix from the real world. Her view of the Matrix would be in green code, but that same view is good enough for Cypher to identify "blondes, brunettes, and redheads" in the Matrix from it.
Even if Dujour didn't hug Choi and expose her tattoo to Neo (and Neo declined to go with them), there's still a good chance Neo would see it when Dujour turned around to walk away from Neo's door and go to the club. Neo would just have to keep his door open long enough to watch Dujour turn away.
Trinity wanted Neo to follow Dujour since she would lead him to a noisy club, which would be an ideal meeting place to talk about the Matrix. But even if that failed (because Neo didn't see the tattoo and didn't go to the club), Trinity still had control of Neo's computer and could try to get him out of his apartment some other way. She could, for example, tell him via his computer
Didn't you see the white rabbit on the girl? Follow her.
Obviously this is less satisfying plot-wise, but it works perfectly well in-universe. Alternatively, Trinity could have explicitly set up a meeting with Neo via his computer, ordered pizza delivery for him and told him to follow the pizza guy, etc. The Agents didn't pick up Neo until the next day while he was at work, so Trinity had all night to get Neo out of his apartment and coax him into meeting her.
Echoing DavidS's excellent comment
"In the draft script for Matrix Reloaded it is revealed that these guys are Redpills, covertly keeping an eye on Neo"
Although it's not official canon (since it comes from an earlier script version, still written by the Wachowskis but unfilmed), we learn in the Matrix Reloaded script v1 that both Choi and DuJour are in fact Redpills, he the Captain of the hovership 'Freedom' and she his trusted Lieutenant. Not only that, but it's made explicitly clear that they were working in concert with Trinity and Morpheus to assess and then rescue Neo.
That being the case, it would explain how Trinity knew that they would invite him to the club as well as explaining how Trinity knew that DuJour would prominently display her "white rabbit" tattoo to Neo at just the right moment.
THEY [Morpheus and Niobe] close for a kiss, when the FREEDOM'S captain suddenly jumps between them. It's CHOI - the NEO's supposed neighbor and hacking financier. Exuberant and oblivious, he joyfully gets in MORPHEUS' face.
CHOI: Bro, you [owe] us your asses! We saved you so hardcore you don't even know!
NIOBE smiles at Morpheus and fades back as BOOTH shouts his own praises. Morpheus turns to his less-mature peer.
CHOI: "So, you think you finally found The One, huh? Another One?"
DUJOUR, CHOI'S LIEUTENANT, pushes into their conversation, looking offscreen.
DUJOUR: Idiot, we helped him find him. Hello, Morpheus.
CHOI: Huh?
He looks at what she's seeing. His gaze halts on NEO. He's concentrating on TANK and his apparent girlfriend, who seems to be consoling him. He turns to see CHOI and DUJOUR, does a double-take, and his jaw drops open.
NEO: You?
CHOI is quick to resume his cool.
CHOI: In the flesh, so to speak.
DUJOUR: Welcome to the real world, Neo. I'm glad you're here.
CHOI: What do you think, Dujour? Should we take him with us?
DUJOUR: Definitely.
This also ties in nicely with the obsession shown by the redpills to the whole "Alice in Wonderland" mythos
I have no basis for this, but if you can hack the Matrix to insert a whole person with whatever armament and clothing you want. Wouldn't it be simple to add a static tattoo to a person, or graffiti on a wall, etc. Further, Trinity was not necessarily waiting at the bar. She could easily have been following, waiting for an opportunity to have a private conversation.
For that matter, she could have been having the console conversation with him from right outside his door on a texting phone. If she saw the rabbit, he likely would also. In this scenario, she didn't know where they were going, or that Dijour even planned to go clubbing. But it did get Neo out of the location were his IP and their conversation could have been traced to.
While I like the "earlier script" answers to this post, I wonder why a different Zionist person or team was any less risky than having Trinity confront Neo at his apartment without all the cloak and dagger.
Edit: Please disregard the placement of the tattoo, my thought developed as I wrote. My point is that I believe the group that Dijour was a part of were not Zionese. While not shown, Trinity observed the tattoo and from a local terminal, directed him to follow it. She did not know where they were going, she just needed him to get away from his IP location. She would have "met" him anywhere. It just happened to be a club.
