Janine, that is so true. At a networking event, if you are in conversation with an interested person and he/she requests a resume, they may be thinking along the lines of "let me see what this person has to offer me" type thing. A lot of people are not in tune with the whole "partnering" idea, and will need to be educated on the whole idea. It may be wise to offer Emailing a detailed resume -- sort of a comfort thing for them, or having one with you in your "little bag of goodies" just in case (I am such a "just in case person").
The flyer idea is a really good tool to take with you to a networking event. After attending my last one, I actually made up a brochure, not specifically about my company, but on what and who Virtual Assistants are and how partnering with one is the way to go. I came up with this idea because many of the people in attendance at this event sort of gave the "what?" look. However, after I got my little time in the sun with them, I could see the sparkle in their eyes, which said "Oh, okay, I like it!" But I thought maybe if I made up a little brochure on the VA industry as a whole, it would be a learning tool and, hey, a way of people to get excited about our industry.
Bottom line, I think each event is a little different. I would take my little bag of goodies along, and once you get the feel of what people may be expecting (or needing), dig in your little bag and pull out your flyer, resume, or brochure, along with your business card. You may as well "WOW" them right off the bat.