A good examination of the oral cavity would be the best way to start, probably. It is sometimes necessary to use anesthesia to get a really good look at the oral cavity in cats. Probably the most commonly identified reasons are gum or teeth disorders. Oral ulcers can sometimes cause excessive salivation. Problems that lead to nausea, such as renal failure or gastrointestinal disease also cause excessive salivation.
Some cats salivate excessively when they are nervous or stressed.
This is a common reaction to oral medications and application of flea control products, too. Your vet can help sort through these possibilities and hopefully find a treatable cause. There are probably other causes. A brief episode like you saw is probably related to ingesting that was upsetting. I have seen this after one of my cats ate a spider.