The reason I brought up riveting is because you can do it with basic hand tools. If some kind of welding would work, yeah, do it the normal way. You aren't going to have propane, though, and insulating gasses might require some ingenuity.

Nobody rivets a bike frame because it's made out of hollow tubes and rivets are designed to pinch flat things together. Rivets are just the wrong tool for the job.

Of the metal-melting joining methods, I guess brazing is probably the most low-tech. Maybe propane would be a problem and you'd have to use some other fuel instead (maybe wood gas?), but it's been a thing since 3000 BC so I'm sure an enterprising person could figure some solution out.

Alternatively, the flux coating on a stick welding rod is apparently made mostly of cellulose, which is less exotic than I expected.

If you can hand file a bearing that runs reasonably smooth, I'm impressed as hell. Definitely somebody can - the first lathe got made somehow - but it's definitely not me.

Behold, a lathe:

This stuff isn't as high-tech as you think.

But never mind that; depending on what scenario we're talking about it seems likely some machine tools would survive (e.g. in rural areas, maybe), so the trick would be to find one and get it running.

Once you're talking wooden sprockets and chains,

I am not. I'm talking about, say, salvaging sheet metal from abandoned cars and stamping chain links out of that. Nobody wants a wooden chain; if you're that hard-up, you'd probably be better off trying to go for a belt drive or shaft drive. Or hell, even a penny-farthing!

If you can hand file a bearing that runs reasonably smooth, I'm impressed as hell. Definitely somebody can - the first lathe got made somehow - but it's definitely not me.

Wood might be an option, and bamboo seems like it would be a decent option. Once you're talking wooden sprockets and chains, I'm guessing your going to end up with a pedal wagon more than a bike, though, because it's going to be pretty heavy.

You need a certain amount of pasture land (and fodder during the winter). If you don't have enough, the grass runs out - that's called overgrazing.

(And because I've had this kind of argument on Lemmy before, imma point out that the animals you eat probably ate staple crops. On this continent, at least, we grain-finish everything)

We can’t just eat it raw in the field. This is nowhere near the same. I can’t even.

No, you gather it, pull off the seeds, and if you want to avoid a lot of chewing, grind it a bit. I'm sure all ready from your local bakery it seems like magic, but it's not.

Humans need to plant specific species that we can digest, and then process it so that we can digest those parts because we can't eat the whole thing, and then cook it. We can't just eat it raw in the field. This is nowhere near the same. I can't even.

You do know wild horses exist right?

*I think I'm just gonna leave it at that.

Personally, what grinds my gears, is every abandoned car's battery still having enough juice to start the engine. Nobody ever needs a jump start.

Although, timeline-wise, most of the show takes place over the course of less than two years. It's not until the middle of season 9, the third-to-last season, that there's a time skip of more than a few months.

Rivets for putting together the frame.

Nobody rivets together a bike frame. Frames are brazed, welded, or (in the case of carbon fiber, bamboo, or occasionally aluminum) glued. The only places I've ever seen rivets on a bike are on the chain, old-school leather saddles, and maybe to attach layers of stamped steel on really cheap brake calipers.

Maybe an endmill or even CNC machine

Or even just a set of hand files.

or welding for the frame (someone else might know what exact kind of welding you need).

More carefully-constructed bikes typically use TIG, and for aluminum you want an AC welder. But who's going to be making a titanium, aluminum, or even fancy steel (with Tange or Columbus double-butted tubes) bike in the apocalypse? Any welding process would work for steel, especially when you're building out of random scrap plumbing pipe or whatever.

Your most realistic options would be stick, MIG, or even just brazing with a propane torch. Or building your bike frame from bamboo lashed together with rope and glued with pine resin.

You're not even saved the trouble of gathering it if there's a snowy winter to get through. Plus, there's shoeing and various kinds of other care to factor in.

There's some around here, and if the apocalypse came I don't doubt people would be riding, but it'd be a one per few families thing.

Cattle would probably be the main beast of burden at first.

Bearings are a massive chicken and egg problem if you don't have one to start with, but in this scenario you definitely start with them. You're probably not going to make the really fancy ones, but a basic roller, ball or journal bearing seems doable. They did it way back in the day, right?

If you were a caveman starting over, a waterwheel has about the needed output. Heck, some of the first metal lathes might have run on those, historically.

Rubber might just be a wonder you'll have to do without, if you're somewhere temperate.

Modern fertilizer and pesticides allow you to get a much higher yield on the same land, and modern farming vehicles allow you to plant and harvest whatever oil crops without an army of labourers. If you had a ton of idle land, because all the urban people are dead, it reduces to the second problem.

Pressing/steeping the oil out of it is another challenge. Probably surmountable, although it's still going to cost a lot more than it does now.

Most of how the world would look, if the industrial base and institutions were gone, can be predicted by looking at places where they were never built in the first place.

Maybe an endmill or even CNC machine, if you're feeling fancy, or welding for the frame (someone else might know what exact kind of welding you need).

During the world wars, there were people converting IC engines to run off of wood gasifiers. For that, you either need the skills and tools to reprogram engine timings, or a carburator, though. Diesels can run on vegetable oil, and EVs can run off a solar panel, or, if still running, a wind turbine.

Horses aren't cheap or free to run, either. No matter what, there will be less vehicles, the ones that do exists will tend to be heavily loaded to save money (like you sometimes see in the third world) and they're going to take longer to get where they're going.

of factory farming, which have massive carbon inputs

The fuel used to run the tractors can itself also be biodiesel.