It's not a bandwidth issue. It's about too many people being connected to the same server using too many processes. There's something called "server load". When things are normal, it should be around 2-4. When it starts reaching 5, there could be a problem. The other day, I had a spike of 300 people and the server load reached 50, very bad.
So... I changed a couple of things in the background processes, and the load seems to be under control. The other thing I changed was to put a maximum load on the server. Now if I get a spike of 100's of people, and the server load rises above a certain number, vbulletin starts sending out the "server busy" message. If you get that message, wait for 30 seconds and try again. Odds are you will get the page to load on the 2nd or 3rd try.