I had a "double bass" washtub for a couple of decades (two tubs, connected) with fingerboard, and found a lawnmower starter cord (the smaller of the two common diameters) about optimum to simulate the lower end of a standard stand-up bass with about a 50 inch long string, but it needed at least 40 or 50 lb tension to get it up to where it would "ring" right. I used an electric fence stretcher for a tuning knob and a 2x4 split lenghtwise and rounded a little for a fingerboard. String tension was high enough that I had to "brace" the tub bottom where the string attached to keep from pulling the bottom out.

That kind of string would not be well suited to a "bender" type bass (unless you're built like Godzilla).

For a "bender" type tub, it's likely that you'll get better control and a wider range of usable pitches with a lighter string with some stretch, although too much stretchy isn't good either. I'd say you should avoid string that "creeps" when you stretch it (like most monofilament line), but when the string stretches a little the diameter shrinks a little which gives a slight additional change in pitch to help with both pitch range and control of pich accuracy.

One exhibitionist we've seen recently used a 5 ft diameter tub and about 1/4" diameter aircraft control cable, with an old doubletree for a pole. He sweated a lot, and needed leather gloves with steel "caps" on the fingers to play it. (I was much less impressed with him than he was.)

For best effect, you need to consider both the string pitch, and the tub pitch as separately adjustable parts.

The string pitch depends on the weight of the string and its tension. The heavier (pounds per foot) the string the lower the pitch. Increaing the tension raises the pitch. For conventional instruments, it's usual to target the tension to about 80% of the "yield strength" of the string, since anything less than that will sound "flabby" at best. For a manually manipulated string like what you're considering, probably 20% to 30% is more reasonable, and should give decent results.

Ideally, the tub should have an "air resonance" near the lowest pitch you want to play, and the fundaments air resonance (its Helmholtz frequency) is proportional to the total cross section of all the holes in the volume, divided by the total volume of air it contains.

You can lower the "tub frequency" by closing off most of the "open side," with only a "tuning hole" to let the air flow in and out. Adjusting the hole size will tune the air volume. YOu'll get arguments about it, but you DO NOT NEED to have a big hole to "let the sound out" if you get the right tuning, since the vibrations of the metal will drive far more "acoustic motion" than you can get from pumping air through a big hole. To get to an air resonance close to the lower third of a stand-up bass range you probably shouldn't have more than 3 to 6 square inches of "air leaks" for a 30-40 gallon tub.

Most builders of "bender" type WTBs ignore the tub tuning, and that's permissible if it sounds good to the builder.

For maximum volume, you need the heaviest string you can handle, but that also means higher tension, so there are definite tradeoffs. You likely can get a better compromise (IMO) with a fiber string than with a monofilament, and for fibers a woven construction probably is better than just a twisted rope.

Obviously, lots of people have built instruments of this kind, and nobody ever built the second best one. You can expect any advice to be contradicted by the next advisor - but that's part of the fun.

John