I'm a construction project manager; I do this for a living. So, here's the deal with kitchens and bathrooms. The low end for bathroom remodels (if you have someone come in and do all the work) is probably $3K - if you use lower-end finishes. And really, the sky's the limit. There are some areas where I do think you can save money, and where it's smart to save money. You don't have to go to a fancy showroom to get your new fixtures. Go check out Lowe's and Home Depot. Get an idea of what various fixtures cost. Do you have an Ikea nearby? They are a great source of inexpensive, but great-looking, fixtures and cabinetry. An architect I work with actually won an award for a kitchen she designed - the home belonged to a chef who splurged on the appliances, and then got all the cabinetry from Ikea - the kitchen was spectacular, and aside from the appliances, cost less than $15K. So there are savings to be had, and nobody would ever know you didn't spend a fortune.
Bottom line, here is my advice:
1) Every quote you receive should be broken down very clearly into demolition, plumbing, electrical, tile, flooring, and then further into materials and labor. I would recommend that you go with a time & materials, Not-to-exceed contract. What that means is that the contractor gives you a "worst-case scenario" quote (the "not to exceed" amount), and what you will actually end up paying is for the actual time and materials he spends on your bathroom.
2) You should purchase fixtures directly, not the contractor. When I buy materials for a client, I mark them up 15-20%. Why pay your contractor that money when you can buy it directly? To be clear, your GC should come with you to the plumbing supply house, or the cabinetry place, or wherever, so that you are both on the same page about what you're purchasing, but if you pay directly you'll save a lot. Shop around to find the best prices on the fixtures you like (use the Red Laser app or something similar - you'd be shocked how much money you can save).
3) Before you sign a contract, READ IT. Better yet, if you have any friends in the construction industry, have them help you read it. You need to be VERY clear about what is included, what is excluded, and what you're agreeing to. Do not sign a contract without a job schedule attached to it, and referenced in the contract.
4) VERY VERY IMPORTANT: Do not EVER pay in advance of work being done. EVER. Ahead of time, agree that you will pay as you go. For instance, your contractor can submit bill #1 after demolition is done. Bill #2 comes when the rough plumbing/electrical (if any) is completed. Bill #3 comes after drywall, tile, and paint are done... and so on. And since you will agree only to a time and materials contract, the contractor will only be billing you for actual time and materials spent on the job so far. It is common to withhold 10% of the overall total until the job is complete to your satisfaction (that means that all the picky details are fixed and perfect).
5) Do not proceed without getting 3 bids (at least) from licensed contractors. Ask for references, and check them thoroughly. Before any work is done, you need to be sure you have a copy of their liability insurance and their workers' comp, with you as the "additional insured." Don't worry - any contractor worth his salt will have no problem providing you with copies.
If you need any help with this, please feel free to PM me. I've been doing this for years, and have unfortunately been called in many, many times to clean up projects that had gone bad - so I know where all the pitfalls are! Good luck!!