Installing Arch without pacstrap is easy. No, you won't use archbootstrap. That is only for chroots. Instead, you will do it hand made.
First, make the file system.
mkdir -m 0755 -p /path/to/root/var/{cache/pacman/pkg,lib/pacman,log} /path/to/root/{dev,run,etc/pacman.d}
mkdir -m 1777 -p /path/to/root/tmp
mkdir -m 0555 -p /path/to/root/{sys,proc}
cp -a /etc/pacman.d/gnupg "/path/to/root/etc/pacman.d/"