If someone was to come at us with their own additional contract, we would probably decide that we had given them enough of our time and move on. As Nick mentions below, the contractors reputation is the one on the line. They have every reason to do right by you. The crooks of the world generally don't have a reputation to stand on, and as a customer it is your job to research who you are hiring. If you can't find anything about them, they probably aren't who you want to be dealing with. If they ask for money upfront, they probably aren't running a stable outfit. We never take a penny upfront. We collect when the job is fully complete even when we are working on weeks long projects.
It's totally legitimate for a professional to charge you for a design, at least in some situations. If the contractor has a book of ready-made designs and just pulled one out to show you, then you're right that s/he shouldn't charge you. But if someone does a design that conforms to your room's dimensions, with the features that you want, then that person has invested time in creating a work product. Some contractors and architects think that's just the cost of doing business, but many others consider that their time is worth something, and they charge for it. You just need to let contractors know that you're not looking for that kind of custom work, and not willing to pay for it.
With the layout in place, you can begin to think about design. Collect images of bathrooms you like, and then find the common themes to determine your style. Are you a fan of modern bathroom design or is a country-cottage bathroom more your style? Do you love the crisp, clean look of a white bathroom or is a bold, brilliant red bathroom more appealing? Heading to the store with a clear vision will make it much easier to whittle down the choices for cabinets, hardware, and other finishes.
The more luxurious the materials for a bathroom remodeling project, the higher your budget will be. Using marble for your counters, custom cabinetry or handpainted ceramic tiles for your new shower walls in the master bathroom will look terrific. But it will also raise your material costs considerably more than installing a laminate countertop and low-end or mid-range tiles.