Why does my tub faucet spit brown water for a couple seconds before it clears up?

That two-second brown burst followed by clear water is almost always the water sitting in the stub-out behind the spout picking up rust. In my house it was the upstairs tub, same deal, only that fixture and only after it sat overnight. When I finally pulled the tub spout off, the threaded nipple coming out of the wall was galvanized pipe, and it was the only galvanized left anywhere in the plumbing. Everything else had been redone in copper decades ago, so that one fitting was the whole story.

Here's why it's only that tub: some spouts, expecially the fancier decorative ones with internal diverter valves and tight channels, hold a plug of water in the nipple behind them when the faucet is off. That standing water sits against the galvanized iron and rusts it. The fittings that drain dry don't do this becasue rust needs constant moisture to keep flaking off into the water. Your crusty white buildup around the spout actually fits this too, since mineral deposits love to form where water lingers. Before replacing anything, unscrew the spout and look at what's threaded into the wall. If you see dull gray pipe with rough, mottled threads, that's galvanized. If it's copper or brass with clean gold-colored threads, the problem is likely just crud inside the spout itself and a good cleaning or a cheap replacement spout fixes it.

If it is galvanized, swap the spout for a plain basic one that lets the stub drain when it's off. The rusting slows way down once the fitting dries out between uses. But don't ignore it long term, because a galvanized nipple that keeps sitting wet will eventually rust through behind the wall, and then you're dealing with a leak inside the cavity, wich is a way bigger job than a two-second brown stream. The fix is a spout swap and maybe fifteen minutes with a pipe wrench or even by hand if it's not seized.

If the nipple turns out badly corroded or the spout is stuck on there, that's the point where I'd get a plumber, but try the pull-apart first.

The part about the white crust on the faucet spout is interesting. I always thougt that was just mineral buildup from hard water, but the rust thing makes sense with where the water sits. If the pipes are old and rusted, does that mean the issue is prolly related to the age of the whole house instead of just this one fixture? I had a similar thing happen on a different old tap a few years ago. I ended up just replacing the whole faucet assembly instead of just the spout. Do you think that's usually better than swapping out just the piece that comes out of the wall?

Had the same thing at my old place, except mine was the kitchen sink that only did it after a weekend away. I pulled the spout apart and the inside was caked with rust flakes, the pipe behind it was brass and totally fine. Tossed the old spout, put a basic chrome one on, and it never happened again. The white crust on yours will soften right up if you soak a rag in white vinegar and wrap it around the spout for an hour before you unscrew it, makes getting it off a lot easier. Also check which side the issue is on. If it only shows up with hot water, run the cold for a bit and see if it stays clear, that tells you something about where the water's sitting.

First time posting here so hope this makes sense. Mine is kind of the reverse situation, the bathroom sink in my basement does this but only on the hot side, and only the hot side. Cold runs clear right away every time. I kept blaming the faucet cartridge but swapping it changed nothing. Now I'm wondering if the hot water line has its own little dead leg somewhere that sits wet. Does that ring a bell to anyone, or is that a totally diffrent beast than the galvanized nipple thing people are describing here? I'd rather figure it out before I start opening up drywall for no reason.

Update: pulled the spout off like the guy with the kitchen sink suggested and the inside was pretty nasty, tons of flaky junk caked in there. Soaked it in vinegar, scrubbed it out, and the burst is way shorter now but still there after a day or so of sitting. So something upstream is still feeding it. Is the threaded nipple behind the wall something I can unscrew myself or is that a bigger job?