Well, Vegeta himself could be seen as the antagonist in the beginning. Since he is the one doing the kidnapping, he's causing distress to Bulma. However, as the story progresses, the real antagonist could turn out to be someone else. For example, another alien race that is after Vegeta and uses Bulma as bait to lure him into a trap. So, it's not so straightforward in a fanfiction.
It's possible that the antagonist could be a new, self - created character in the fanfiction. This character could be a mad scientist who has been observing Vegeta and Bulma. He wants to study their unique relationship and powers. So, he manipulates Vegeta's mind just enough to make him kidnap Bulma so that he can observe them in a closed - off environment. This new character would then be the source of all the trouble in the story.
One possible plot could be that Vegeta kidnaps Bulma because he believes she has some technology that can help him gain an edge over his enemies. He takes her to a secret location and demands she work on it for him. Bulma, being the feisty and intelligent woman she is, tries to outwit Vegeta at every turn while also gradually getting to know a more vulnerable side of him that he doesn't usually show.
There's a possibility that it's a dark wizard - like being who has created this burning black energy as a weapon. He might have some vendetta against Bulma because of her scientific achievements that he sees as a threat to his magic - based power. And Vegeta gets in his way when he tries to harm Bulma, making them the main targets of this antagonist.
It might be a new character created specifically for the fanfiction. Maybe an alien race that has a vendetta against both the Saiyans and Earthlings and sees the union (even if it's just a meeting) between King Vegeta and Bulma as a sign to start a conflict.
Frieza or his remnants could be antagonists. They might see the unborn child as a potential threat in the future, especially if it has strong Saiyan powers. So they could plan to attack Bulma to prevent the birth.
It could be another dark guild. They might be using Gray as a pawn to kidnap Lucy, perhaps because they know of her celestial spirit magic and want to use it for their own evil purposes. Gray may not be fully aware of their manipulation.
It could be Aizawa himself if he's being controlled by something or has some sort of ulterior motive that is not in Izuku's best interest. But if not Aizawa, then there could be a hidden villain who is manipulating Aizawa to kidnap Izuku.
It could be a new, powerful dark wizard who has a grudge against Fairy Tail. This wizard might manipulate Natsu into kidnapping Lucy to create chaos within the guild. The dark wizard could be after some powerful magic that only Lucy can access, and by kidnapping her, they hope to force her to give it up.
It could be Orochimaru. He might have manipulated Kushina into kidnapping Naruto. Orochimaru has always been interested in the power of the Uzumaki clan and Naruto's nine - tailed fox power. He could be using Kushina as a tool to get to Naruto.
There could be a rogue Saiyan who has different ideals from Vegeta. This Saiyan might think that the baby should be raised in a more traditional, warrior - like way and try to take the baby from Bulma and Vegeta. Or, an evil scientist who wants to experiment on the baby's unique Saiyan - human DNA could be the main antagonist, creating all kinds of challenges for Vegeta and Bulma to protect their child.
The story might center around a new threat to the Earth that only their combined efforts can defeat. Vegeta uses his fighting skills and Bulma uses her intelligence to create new gadgets or find weaknesses in the enemy. Along the way, they reaffirm their love for each other and strengthen their family unit.