In Thor 3, why doesn't Hela use a spaceship to get to other worlds instead of relying on the Bifrost. To return to Asgard Thor and Friends used a spaceship. Did Asgard not have spaceships?
Because it would take a long time to get anywhere.
When Thor is planning to leave Sakaar, Valkyrie begins to tell him how to get from there back to Asgard. Using her spaceship, she predicts the fastest they could get to Asgard is 18 months. The reason Thor and Loki manage to get back sooner is that Heimdal tells Thor the "big red one" is faster, but not every spaceship can make the journey.
The Bifrost, on the other hand, is instantaneous and can go anywhere directly point-to-point. Hela is clearly impatient and wants to go start conquering worlds now. On top of that, as a military weapon, its strategic use is immeasurable. She's not just angry because she can't travel off-world quickly, she's angry because Skurge lost one of her greatest assets.
(There are a few other ways to get to/from Asgard quickly, but they're not very convenient. Loki knows some secret, presumably magical, way but it's possible Hela doesn't know about it. Odin also managed to get Thor to Earth once but it took a lot of energy, and Hela may not be strong enough yet.)
The Bifrost is the only publicly-known way in and out of Asgard
This was a plot point in the Dark World, and possibly also Thor.
There is a hidden way that Loki knows, but it is well-hidden and there is no reason to think that Hela would be aware of it.
Hela used some kind of teleportation for herself to come to earth the first time, when she broke Thor's hammer, but I think Bifrost is faster and easier to use when it comes to teleporting Hela's army.