can I make my bot/bouncer/whatever start automatically when s0 reboots?

Yes.

Edit your crontab using crontab -e and add a line like this:

@reboot eggdrop /home/milki/milki-barwench/eggdrop.conf


This will run the command eggdrop /home/milki/milki-barwench/eggdrop.conf whenever s0 reboots.