I am currently using Windows Vista and Linux Ubuntu (I'm not 100% sure which version).

However, whenever I start up my PC, I get greeted to the HP BIOS screen, and then after that, I get the Windows Bootloader.

Now, this is where things get interesting:
If, on the Windows Bootloader I select Microsoft Windows Vista, it loads Vista.
If I select Ubuntu on the Windows Bootloader, I get treated to a second bootloader (I assume the Ubuntu Bootloader).

I'm wanting to remove one of the bootloaders (keeping Vista as my primary OS, but still having access to Ubuntu in the bootloader). As a result of this, which bootloader should I remove, and how would I go about removing such bootloader?

If you intend to keep the Windows bootloader, then you can simply set the Ubuntu's bootloader to boot immediately into Ubuntu without showing you the menu. This can be set in /boot/grub/menu.lst on Ubuntu 9.04 and older. For Ubuntu 9.10 & newer it can be set in /etc/default/grub
This way, it just removes the annoyance of having 2 bootloader menus.

You really don't want to do that - better to hide the grub menu. Run "lsb_release -a" from a terminal so we can offer meaningful advice.