Something we were doing when I had a web design agency was to have awesomely beautiful and detaild proposals where we summed up the context, constraints and goals of the project. We considered them as our first deliverable and spent time creating beautiful indesign templates. It allowed us to stand out from the start.
Another thing is while our competitors were usually not showing anything yet at this bidding stage, we were already delivering some high def mockups, sometimes within the weekend.
Last thing, we didn't have any sales people. Meetings with leads and customers were directly being handled by tech leads and lead designers, who were not there to sell, but to advise and find solutions with the client, explaining and integrating the client within the process from the start.
All in all, we won all the biddings at the time despite being usually 30% more expensive.
Something we were doing also is to include free perks that didn't cost us anything and was making a lot of difference for them ( free access to our email marketing platform, server monitoring, etc... ).