How Google Trip Bundle works?
Company secrets - Google does not disclose what they actually use. Any answer to this is pure speculation.

It probably is not even just "one" algorithm, but many. But it may be as simple as finding overlapping dates and locations, assuming that people cannot be in two places at once. You could test this: book a flight, and a hotel on a different destination during the same time interval. I wouldn't be surprised if they nevertheless show up as one "trip" (and it doesn't really degrade user experience much).

It will very likely be a supervised approach. Which does not mean "interactive". On the contrary, unsupervised approaches will likely need interactions to choose parameters. Using some training data (e.g., from employees, or user interactions) to improve matching quality looks promising, though.