My anti-hero is good character; my female antagonist is the threat. How can I express a romantic relationship between them if I write a short novel? I am a new writer with almost no experience. I have never had a relationship, so it’s hard to me to write this.
This is, in it's current state, a very broad question. That said, I believe that with a bit of tweaking it can avoid being closed and also end up useful to others, so I'll attempt an answer.
The first thing that you need to do is decide on what the dynamic of the relationship is and what the end-goal of your plot/subplot is. Then consider the following:
Is this a mutual relationship? - By this, I mean are both parties invested in this relationship. Are both in love/lust with each other? Or is one party trying to win the affection of the other?
Is this an existing relationship? - Is it already established? Newly formed? Or is it being established through the course of the story.
Is this a happy ending? - At the end of the story do the couple stay together? Is one lost? Do they end it - and if so, is it amicable or not? Or, does it take on a Romeo and Juliet spin, and end in tragedy for all involved?
Is this a story about redemption/salvation? - Does the "evil" love interest end up being saved by (or saving, for that matter) the "good" character? Does either change their way?
These are very, very broad questions, but can help you to flesh out your characters. The biggest caveat I will add, however, is don't throw in a relationship just for the sake of having one. Give it a purpose. Make the characters and the readers invested in it.
And most important of all - get out there and read how others have handled it. Nearly every YA novel on the market has some kind of relationship in it. The Hunger Games, the Divergent series, Harry Potter - all have relationships and romances between characters. Read them, take note of the evolution of the relationship, the view of it from those involved, the impact that it has on the individual characters (if your anti-hero and antagonist come into conflict, how will they react? If one is in danger, will the other sacrifice themselves?), the effect it has on the stories.
In broad terms this depends on what you think of as "romantic", whether it is just sexual or they truly enjoy each other's company outside of the bedroom.
An easy way to accomplish this is to refer to a previous history: Your hero wasn't always a hero, and your villain wasn't always a villain.
I understand if you've never had a relationship; but most adults IRL have before the age of 22 or so. So it is plausible neither of these characters is virginal and it could easily be they were mutually first-time lovers back in high school (or generally as teens, depending on the time period you write about), long before they were either hero or villain.
You say you have an anti-hero; that implies flaws: Perhaps as a teen these flaws were much more predominant and that is what attracted her, and what she loved about him. So they are still in touch (literally and figuratively), still hooking up, but she is hiding her true self from him. In the years since their first experience, he has been tending toward the good, but she has gone deeper into her dark nature than he knows, and has been lying to him about that for years. He knows she has dark thoughts, but he thinks it is just a fantasy of hers like playing an evil character in a role-playing-game; he doesn't know exactly what she has done in real life.
This relationship makes it more plausible that recently, something new has come along (The Big Story Problem) that is going to put them in conflict. Just because they are sharing the space. He feels compelled to help people, she sees a chance to exploit those people and get rich or powerful or whatever you are making her want.
Without your own romantic experience, you need to study (watch or read and think about) how other writers (for film or print) have portrayed romances. You don't want to plagiarize them, but keep yourself "above the story" and generalize what they did: what kinds of settings worked? What kinds of lines worked? How do other authors avoid writing porn (which I assume you want to do, lacking experience), and skip over the scene where they get naked and have sex, but still make sure the readers understand the characters did?
Many other authors have distilled their own real romantic and sexual experiences for you; if you read enough of these, treating them as textbook examples; teach yourself some "rules" they seem to follow, you can write a plausible romance scene or sex scene.
Or you can try to make it up: Most authors write successfully about murders, torture, heists, bank robberies, rapes, kidnappings and many other topics without ever having done or experienced them. So it is possible, but I think it takes being able to read what others have written while not getting emotionally immersed in their story, but staying analytically above it and trying to notice their writing craft: What they are telling you, and what they are leaving out, or glossing over, or just jump-cutting over.
"How do I write a relationship" is a very broad, and possibly tough question, especially if the author never had a relationship (sorry to hear that). I suggest that you study existing examples and try to avoid cliches.
The former ("Catwoman") is more of a genuine romance, when female antagonist is not without redeemable qualities, and your characters have respect for each other. Your reader may end up rooting for the antagonist and want to see the romance to go on.
The latter ("Villianesses") is more of a one-sided seduction, where antagonist can be purely evil. The reader would likely be dismayed by a romance like that, but this may allow you to be creative with plot twists.