You are correct. Microsoft doesn’t make a Mac version of Access, and while there are some database programs for the Mac, there’s nothing I know of that’s exactly like Access or is fully and easily compatible with it. You could install Windows on your new Mac and boot into Windows when you need to run Access. In my tests of Apple’s Boot Camp software for running Windows on a Mac, Access ran quickly and well.
However, I suggest that you avoid the Mac and buy a Windows machine. If your main use of your computer is to run a single program that only works in Windows, that means that, even with a Mac, you’ll be spending most of your time in the Windows environment, and won’t gain many of the advantages of the Mac operating system and its tight integration with the Mac hardware. So, you might as well just buy another H-P or a Dell or Lenovo.