In IT it's different. 9/10 software development, DevOps, System/Network/Security Engineering, and so forth jobs I've seen have required just a bachelors degree. Other fields are likely different.
It's not like its impossible to get a job with a bachelor. Almost all companies and institutions will just automaticity look for master graduates, and you might have to educate them about the benefits of getting the same capabilities for a lower pay.
I don't have any statistics on this, but when I studied computer science 20 years ago, nobody stopped at the B.Sc. Depending on the university, it's basically only another year, writing one or two papers, and then a year, either doing the same or the equivalent of a minor, where you're just doing the first year of the B.Sc. in some other field.
One issue you might encounter is that Danish IT companies are obsessed with hiring people with a masters, even if the job doesn't even require a B.Sc. Most of the jobs in the industry could be fulfilled by people from trade-schools or other shorter educations. Companies just seem to have this idea that they need engineers or people with a masters in computer science, even if their product is just some CRUD application.
Things have changed. You can get far with just a bachelors degree, if you are open to working other places than Big Four and corporations with tens of thousands of employees. I have anyway, and I'm only 10 years behind you. If you move into InfoSec the requirements for degrees are even smaller, at the end of the day.
Also how much is a masters degree even worth after a handful of years of relevant experience anyway? Not much...
