My strategy with bid negotiation was to only solicit bids from subcontractors who were highly recommended by trusted sources. That way, I could hopefully focus on price without worrying I was getting bids from guys who do shoddy work. In most cases, I adhered to this strategy, although occasionally I got a bid from someone brought in by a related subcontractor (e.g., a heating guy who got a bid from a plumber friend).
In most cases I got at least three bids. I plotted the results of this bid process for the major subcontractors involved in the first phase of my project. These are the costs to do the work, including materials (except for framing, which is labor only). My house is about 3,700 sq-ft of living space with a 600 sq-ft garage. The flatwork quote includes all the concrete floors in the house, a concrete driveway, tinting the concrete, and applying acrylic sealer.