You can never 100% eliminate customers shopping or trying to renegotiate the deal. Some people just have to push all the time and try to change things to get as much as possible for as little as possible.
What I have found that works for me is not “bidding” jobs. You can only bid jobs that have a design so everyone is bidding on the same thing. Otherwise you will get three companies throwing out numbers and you will get three different numbers on three very different systems.
Work like a design/build architect. Show them what you can do for them and then offer to design a system for them at an agreed upon ballpark price. They pay upfront for the design. After you are done they get the design and your price for the build. If they want to have another company bid on the job that is fine, if they want you they pay your price. Explain that you are not selling parts you are selling a full system, if they want another companies parts price they can also have that company put the system in. Almost all small businesses work this way.
Doing business this way means you will not get every job from every client. You only really loose the time you spend on the initial meeting. You don’t lose the hours of work giving them a free shopping list or worse taking an unprofitable job. If someone is not willing to pay for your time to design a system they either don’t like your work or they are unwilling to pay for quality work. It is getting much harder to find people who want quality but I would rather have no work then have unprofitable work.