There is suddenly silty, grey, dirty water coming out of my bathtub faucet. And the toilet bubbles when I drain the water. What does this mean?

If you have described this correctly theses are 2 unrelated issues. The toilet is saying the vent stack is partially clogged and needs rodding. The dirty water, is it present when you run just cold and then just hot water?

Thanks for your response. I just filled the bath with a mix of hot and cold as I do every morning and it came up really dirty and left a silt when I drained it.

The silty stuff, could it have possibly come up through the tub drain? I think you have drain pipe clogs. Try collecting hot then cold water in a bucket to see if the bad water is coming from the spigot

I had shut the drain, just as you would do when filling a bathtub. I'll collect water from both and see what it looks like. Hmmmm. Thanks for answering. Can NOT afford to call a plumber!