HBC (that's the most common abbreviation for Homebrew Channel btw) will work just fine with nothing other than an "apps" folder on your SD card with the apps setup in it.
For BootMii, all you need to do is run the HackMii Installer and choose the option "Prepare SD card" under the BootMii menu. You don't need to use Letterbomb again, all you need to do is download HackMii Installer from here: http//www.bootmii.org/download , then make a folder in your "apps" folder called "hackmii_installer" and put the boot.elf from the download in that folder. Then it should show up in HBC. Run it from there and prepare your SD card, and BootMii should work again.