It is rare that a photographer will shoot studio portraits using a bare flash, but that does not mean you can't do it. In fact, you might be surprised by how you can accomplish with a bare flash, and the skills you will learn in practicing this will come in handy in a wide variety of situations outside the studio.
Coming to you from Lindsay Adler with Adorama TV, this excellent video will show you what you can accomplish when using a flash with no modifier. Generally, modifiers are used both to control the shape and fall-off of the light and to turn it into a larger source for softer, more flattering light. However, a bare flash can be more versatile than just functioning as a tiny source aimed straight at the subject. By learning how to bounce and diffuse its output, you can get a much wider range of results. This skill is especially useful for professionals who might not have the luxury of working with modifiers (wedding photographers, for example) and will help you improve your overall understanding of the way that light behaves. Check out the video above for the full rundown from Adler.
Not to split hairs, but the curtain sheers are a modifier and might cost as much or more than a cheap umbrella..
I think the idea is more people are likely to have sheers laying around at home than a photography specific umbrella. Likewise a shower curtain, sheet or other home good.