Your job is to keep them intrigued until it is complete. They may be annoyed to arrive at the screening and see their competitors. But this will get their competitive juices flowing. They will know that they better make a decent offer quickly if they hope to get the film. Retain an experienced producer's rep or entertainment attorney to negotiate your deal.
Filmmakers know about film, distributors know about distribution.
Don't kid yourself and believe you can play in their arena and win. There are many pitfalls to avoid. Get yourself an experienced guide to protect your interests. Any decent negotiator can improve a distributor's offer enough to outweigh the cost of his services. Always check the track record and experience of each distributor.