What will happen if you leave a tarantula bite uncleaned for three days?

Probably nothing because you would ordinarily have experienced symptoms that would make you seek medical aid by that time if any infection were going to cause big problems. Just keep an eye on it.

Tarantulas bites are made with fangs that are not very big around. Wounds that are produced by tarantula bites are mechanically similar to getting stuck with a sewing needle or stepping on a thumb tack. The greatest danger of such a bite is that it might introduce tetanus into the body where it could thrive. The reason that rusty nails are dangerous is not because of the rust but because the roughened surface of the nail makes it more likely to carry tetanus along with it. Shiny nails carry less dirt.

A very few kinds of spider bites are suspected of introducing bacteria such as staph and causing necrotic lesions. Tarantula bites have not been implicated in MRSA or other such infections. Tarantulas do not consume dead prey. They eat fresh, clean insects that typically are not carrying any microbes that could infect humans. Tarantulas keep themselves clean.

So, since the bites seal themselves and generally do not carry any microbes that produce diseases in humans, they are not highly likely to carry disease. Since the wounds seal themselves, any treatment that is going to be effective against anything carried into the body by the bite would need to be done quickly. Some disinfectant such as buffered iodine might have the best traits for getting carried as deeply into the wound as possible. Antibiotic salves would tend to seal microbes in, and would have no effect against viral diseases. Soap and water would be better than anything greasy.

No cleaning done to the wound after it stops bleeding on out to three days or later would be likely to make any difference. Any germs are already on the inside where cleaning won't reach them. (If a wound bleeds at all it would be a good thing because that would wash the wound from the inside out.)

If any harm, beyond envenomation, were to result from the bite, it would probably show up with the same symptoms that an infected needle or nail bite would produce. It would probably produce symptoms such as turning red, feeling warmer than nearby unaffected skin, pain, itching, etc. in a matter of hours rather than days. These symptoms would, of course, be similar to reactions to some tarantula venoms, but venom symptoms should gradually get better. If no signs of infection have been observed after three days, probably nothing will happen. (There are exceptions, as always, so one should be remain alert for signs of trouble.)

Any time a wound shows signs of infection it should be kept under observation. Getting progressively worse should be regarded as a sign that medical treatment may be needed. Salves, creams, etc. applied on the outside generally cannot be trusted to have an effect deep within the wound.