An invariant is relationship between two things that must always fall within a certain range. For example, a soccer match must have two teams else it's not a soccer match.
In the examples of auctions and bids, you can have an auction that has no bids. When an auction starts, there are no bids placed. So in most auction domains, I don't think an auction have at least 1 bid would be an invariant.
Invariants aren't necessarily business rules, they can be facts about he problem domain as with the soccer match example I gave.
Thanks for posting your question.
Hope that helps