It may be possible, Joan, but it's a long and difficult process. It does require, I think, some background in refinishing and a refresher course in chemistry. Unless you have done some similar projects, have good gloves and eye protection, with a good safe place to work, I certainly would not encourage it.
If you feel that you qualify, search using my name. You might be able to find the info on the web. You are correct that I am making it difficult to get the info. If you aren't serious enough to do that, you will not be anywhere near serious enough to complete the bleaching and refinishing process.
I would also suggest that you find out what kind of wood it is, or if it is real solid wood at all.
If it is not real solid wood, consider painting it and the instructions and cautions for that are on the *** **** knowledge base. You should be able to tell what kind of wood it is by looking at the material from inside the piece by removing the draws, or from the edges on the back of the piece.
One further comment is that modern furniture makers use some really dangerous chemicals in their finishing. They can do that because they are equipped to handle them safely and the manufacturers will not even sell these products into the consumer marketplace. What they accomplish is to take inexpensive and not particularly pretty wood and make it look like beautiful and expensive wood. Do you know or care if your Thomasville dining table is poplar? Not as long as it has it's Thomasville finish. But if you strip and refinish, it will just be poplar and not give you the look that you will expect for all the work of bleaching. I'm not picking on Thomasville. They are the best at doing that, and it works fine for most people!