I managed to get an Apache 1.3 Bugzilla installation setup. This is possibly incomplete, and does not aim to be a thorough explanation of how to set it up.
OpenBSD runs Apache in a root jail, at /var/www. It can get a little confusing at times where the configuration files and documents go if just starting. Because of that, a few things happen: some files like SSL certificates, are on the root filesystem, and some binaries are copied from the filesystem into the jail, such as perl or mysql and their libraries.
First, see the OpenBSD MySQL docs on how to setup the database server.
Second, copy some necessary libraries into the chroot. This list is probably incomplete, excessive, or both:
mkdir -p /var/www/usr/lib mkdir -p /var/www/usr/local/lib/mysql cd /usr/lib cp libc.so.73.1 libcrypto.so.23.0 libm.so.9.0 libperl.so.14.0 libpthread.so.18.0 libssl.so.20.0 libtermcap.so.14.0 libutil.so.12.0 libz.so.5.0 /var/www/usr/lib/ cp /usr/local/lib/mysql/libmysqlclient.so.23.0 /var/www/usr/local/lib/mysql
Bugzilla itself is really simple to setup. Unpack the bugzilla tarball into the directory where you want it to run. Once there, you will need to install the Perl modules that it needs.
Bugzilla makes it easy by downloading and installing the modules locally to the installation, meaning it doesn't need to use the system modules. To make things equally simple, just let bugzilla install the necessary modules, instead of manually reviewing them:
perl install-module.pl --all
Once everything is done, edit the localconfig file and make necessary changes for database user, password.
Then check the configuration file and go from there:
perl checksetup.pl
Bugzilla is going to run perl as a CGI binary. Setting up the system with mod_perl is possible, in theory, but I've never been able to get it finished, so this is a simple fallback.