Do spider bites stop progressing after taking antibiotics?

Only if infected.: Antibiotics should do nothing for a spider bite unless of course it is infected. This is not common, but can happen. I suppose that if you had a spider bite and you took anything and the bite regressed as it was wont to do, you could attribute succes to the ingested agent.

Timing is everything: If by "spider bites" you mean boils or abscesses (which people often mistakenly assume are spider bites), the answer depends on timing. If caught early enough, an antibiotic can sometimes keep the abscess from forming. But once there's a collection of pus under the skin, it's too late, and drainage is usually required.