If make is reporting that there is a bzImage, then it seems to me that all you have to do is copy that file to the name "vmlinuz" and put it where your boot-loader can find it. Update the appropriate config files and re-run the boot-loader. Since you didn't say which loader you're are using, I can't help you with that.
What distro and kernel version are you using, by the way?
Also, vmlinuz doesn't really have to be named anything in particular as long as your config files agree with whatever it's named. It does have to be a bzImage format file though, because of certain limitations of the way PCs start in "real mode".
Ok, I've found out a few interesting things that I was wrong about. I have removed them. You can find the correct information by going here:
I sincerely hope I didn't confuse anybody too much. Apparently, my mistake was a common one.