I have the latest Mac OS X Mavericks installed onto a hard drive which I can boot from. As I mainly use a Windows machine, is there a way to boot up the hard drive in a virtual window on Windows, without having to reboot and change the BIOS drive boot order to access OS X Mavericks?
First, understand that the Mac O/S is licensed only for use on Apple hardware, and as such doing what you want to do is not exactly legal...
Generally speaking it is possible to virtualize the Mac O/S. I, myself, have done this using Virtualbox and an older version of the O/S so I can run some older applications. That said this has been virtualized on Mac O/S, not in Windows like you want.
However it should (YMMV) be possible to take a VM created in Virtualbox on a Mac and copy the files to a PC and run them in Virtualbox on a PC.
However using an installation of Mac O/S on a physical hard drive, I kind of doubt it as PCs have no native way of reading or writing to HFS+ formatted disks. And it is likely that you have to install the O/S within the VM for it to work there.
Also you need special bootloaders and the like to run the Mac O/S on PC hardware. Such is called a Hackintosh and setting up the O/S to do so is a bit of a black art. But plenty of people do it. A bit of searching should pull up relevant links.
There are applications that will let you convert from physical (hard drive) to virtual (VM hard drive file) but I have no experience with that. It might work but depends on your interest in spending the time trying to get it to work.