It's a movie/TV trope that people can talk to each other and even whisper on commercial airliners in flight. In a story, it’s pracical to confront the reality of the experience and have characters have to deal with the noise when flying. But, how does a private jet compare? Will an intern flying with the big boss for the first time find it refreshingly better, or even worse, or what?
It's certainly reasonable to think a business jet cabin is quiet. Several business jet makers pride themselves on having models with quiet cabins. It varies a lot depending on the business jet, and exact numbers for the cabin sound level aren't usually listed. It varies for airliners too with the A380 being an example of a very quiet jet and the 777 being noticeably louder.
If you're on a luxurious G280 or G650, the sound level would be relatively very quiet at less than 50 db (unofficially). Even other private jets from my limited knowledge allow you to have conversations at even a few feet of distance without much struggle. If you were operating an old loud engine like a Learjet 24 (which actually had turbojet engines) or a GII, the sound would probably somewhat limit conversation.
Exact sound levels are hard to find, in part because measuring a consistent sound level depends on so many factors, including cabin configuration, airspeed, engine thrust, air conditioning status, and position inside the aircraft. Engine loudness, which is only part of the picture, is well studied and published (example).
Loud jet engines are rarer these days thanks to variety of factors, including the fact that operating loud jets is just plain illegal nowadays in many countries. They actually make hush kits for older engines to get them down to legal levels.