In Dungeon World, when the players fail their rolls, things proceed as the GM wants.
Some initial comments before we get to the meat of this.
Dungeon World isn't super great one-on-one. The book itself talks about 2-5 player characters, best with at least 3. You have the player or players you have, but a single player is missing out on fleshing out a backstory through bonds, as well as helping and being helped by aid rolls, and with a single player there are many fewer hit points and other resources for the GM to use up before hitting more lasting consequences. Adapting to a single player is a topic for another question, but just be advised that you should probably be making some extra things up when you go there.
Turn 1 vampire is not the best move here. Especially if you're playing an introductory game where you're using this vampire attack to teach how the game handles violent conflict and what damage is. Vampires are d8+5 damage piercing 1; depending on their initial stat choices, that is possibly one-shot range for an immolator, and almost certainly two-shot range. That'll very quickly remove your ability to deal damage as a way to use up your players' resources rather than end their games, and as the most close-to-hand move to make in a combat scenario you don't want deal damage off the table that quickly.
Presuming player success can be as much of a pitfall for a GM as presuming player failure.
That's an important corollary to playing to find out what happens. It's obviously a bad time if you come into a scene fresh and assume all the players will be okay with hopelessly losing. But it's just as bad to set up a scene with no outcome in mind other than the players winning. Then you drop in a creature which only exists to kill and die, because "the players are going to win the scene", and then the players have a run of bad luck and what's your creature going to do now? Not kill?
If you don't want characters to die in an introductory combat, give them combatants who don't want to kill them. A goblin scouting party, say, willing to risk their lives to steal food and supplies from travelers. They'll certainly lash out if they're cornered, to secure a retreat, but the way you want the scene to go - the way you want the goblins to want the scene to go - is that they all escape into the night with a significant portion of the party's supplies and nobody has to die. So when your party's poor rolls give you a chance to make things go the way you want, that's what you work toward.
Really, though, pretty much every creature can join the Don't Want To Kill Them Club. That's another one of your responsibilities: give every monster life, know what they want when they show up in a scene. And the vampire's most of the way there already. Its instinct is to manipulate, it has moves to charm someone and retreat to plan again. If a vampire has someone at its mercy, is it always going to want to kill them? Or could this happen instead?
And suddenly they're right in front of you, their eyes shifting, whirling, alive in their own right, red within red within red-
And then you're looking up at the sky. The stars have moved. The moon has nearly set, and your mouth feels like someone's packed it full of cotton wool. Oh yeah, and the vampire has a marker on you.
The GM holds up an index card with "VAMP'D" written on it in big friendly letters. Unless you can find a way to rid yourself of it, I'll call it in at some point, and you'll do what the vampire wants. Sleep tight!
And the scene ends in the vampire's favor! It's important as you continue playing to consciously develop a sense of when a scene should end, when the action is starting to wear out its welcome and there's very little new to discover, as well as how a scene should end, so you can bring it to a close with all the players feeling like it ended like they wanted, or at least like they had a fair go but ran out of chances to make it end differently.
Exploit your prep.
Also keep in mind that line in your move palette that says to use a monster, danger, or location move? That means any monster, danger, or location move that's in your prep, not just the ones that are right in front of you in the scene. So if you're looking to have a scene break to your players' detriment and you've got an Ambitious Organization that wants to buy out important people, guess who just jumped in to get you away from the vampire, and is now demanding a blood oath in exchange for treating all your wounds? If you've got a Cursed Place seeking to lure someone in, as you're fleeing from the vampire suddenly your foot finds empty air, the ground comes rushing upward, there must be a sinkhole in the forest floor, but where's it leading?
In these ways you can give your player or players the setback the dice have unfortunately granted them, but still keep the story moving forward.