The bout manager's job is to preserve the integrity of the bout and to assist the MC in off-stage duties. There's no stage time unless the MC asks you to do the warm-up poem.
In most cases, this means the BM is responsible for selecting judges before the bout, corralling performers and judges throughout the bout, managing/utilizing other volunteers (runners, scorekeepers, etc.), and watching the bout carefully for rules violations --or perceived rules violations. In some cases, the BM also might check score math, help with mid-bout rule or rotation clarifications, prepare letters for the bout draw, bring the MC more beer, but not too much beer, etc.
Obviously, a good working knowledge of the official rules is helpful, as is a willingness to approach strangers and ask them to quantify art. And outside of Erik's gratitude, it's a largely thankless job; however, if you like being responsible for a good show, or plan to MC someday, I highly recommend it.
This might sound corny, but I think it is super-fun to be behind the scenes at NPS or IWPS. Competing at a large event is exciting, but the bigger the slam, the more intense the pressure... Volunteering at these events really put a different spin on the fun for me. And regardless of who wins, anyone involved in managing a good bout properly can leave the venue feeling great.
ANYONE who is even thinking about doing this should let Erik know. It's way more fun than you think work should be.
(Also, Ransacked? I will totally be your reference.)