How hard is it to get into graduate school with just a bachelor’s degree (in any major)?

If you are American, this is the norm for all forms of graduate study.

You can earn a master’s degree before earning a PhD, but you generally don’t have to, and if a school has a good PhD program in a subject it probably doesn’t offer a standalone master’s program in the same subject.

And of course for professional master’s degrees, the norm is the same.

In Europe and elsewhere, it is normal to complete a master’s degree separately from a PhD. And if you did not earn your bachelor’s degree in the US or Canada, you will probably need a master’s degree if you want to pursue a PhD even in the US.