I'm in your shoes. Bidding basic residential is VERY hard for me also. So far I only dare to go T&M and risk losing the work.
In an estimating and bidding course I took many years ago it was stated that if you get 20% of the jobs you bid on you're doing ok. I've been doing T&M work on new homes for a few years, but I do give them a "ballpark" price first. Sometimes the ballpark price scares them away, sometimes not. You win some, you lose some. Many customers just worry about price and nothing else. As soon as they start talking about taking out their own permit and hiring a moonlighter to do the work, there's no point in even bothering to bid. A legit electrical contractor cannot compete with that. I have a letter I issue with my estimates stating that price is only a small portion of what should be considered when awarding a bid. Warranty, quality of work, how long the contractor has been in business, reputation, licensing, insurance, worker's compensation, etc should also play a part in selecting a contractor. A lot depends on the economy of your area, how much construction is going on and how many contractors are available to do the work.