You could always rent a snake.

I couldn't get the snake that I have more than a foot down the overflow. I don't know why.

You could try an air blast plunger, or one of those single use cartridge type systems. But to make these things work, or to get full effect from even a normal plunger, you have to block the overflow drain effectively. To do that, you may need to remove the overflow drain cover plate, and stuff up the hole with a wet rag, even having a helper continuously apply pressure to the rag bundle to get better sealing of the overflow.

Failing that, a power snake is your next move.

Sometimes, a ton of plunging, even with an unblocked overflow drain can be effective in breaking up the clog enough to get at least slow drain action. What you're doing is trying to get vigorous plunging action to force jets of water down the drainpipe enough to agitate the clog from the effect of momentum on the water column. You never really get much pressure on the clog due to the unblocked overflow, but the agitation of the water column is sometimes enough to move enough of the clogging material so that slow draining begins. At that point, you can reasonably use enzymatic or chemical drain cleaners, since the slow drain action can carry them to and past the point of clog.

Pour a couple of cups of borax into the drain and see if that works. I've cleared hair-blocked drains that way. But be careful, it's caustic and can burn. And do not mix with bleach.

Has one of your neighbours been killing people? Maybe you should ask them!

Also, sometimes pre-compressing the plunger cup, and sliding it over the drain opening, and them pulling up to use it as a "sucker" can be more effective in pulling up debris material than trying to push it through the drain with plunging. If you do get up yucky slimy or solid stuff, bail it out to the toilet with a plastic cup or something, and run clean water to provide working fluid for your plunger. Don't keep sending material you've actually pulled up back down to clog!

I think those are all the tips I have for tub drains, but even if I think of something else, I'm shutting up now...

If you do manage to plunge it (or otherwise non-chemically unplug it) to the point where it drains, even sluggishly, and you're still looking for a chemically neutral way to get it draining quicker, try this:

Boil a big pot of water. Pour the water directly into the drain.

Wait five minutes, or as long as it takes for a second pot of water to boil. Pour it directly into the drain.

It melts the fats that hold the clog in place, and may help clear it. If not, at least you won't have a pool of Drano sitting around.

Sometimes tree roots get in between your tub and the rest of the sewer.

Does your toilet bubble and act weird when you plunge the tub?

(Oh, and do you have a septic tank? IF so CALL PLUMBER NOW.)