Former airline pilot here …
As others have said, the typical bizjet is not materially faster than a typical Boeing-size airliner.
The RJs are generally a bit slower, with typical cruise speeds of Mach .70 to .74. Current Boeing / Airbus narrow-bodies are .74-.78, and the big guys other than 747 do .78 - .82. A 747 wants to go fast, more like .82- .85.
And, as noted above, in general we run at an economical speed, not absolute max cruise speed. The difference is significant, generally .10 to .15 Mach. So the numbers quoted in various non-specialist sources can be hard to compare unless you know what sort of value they’re quoting. My numbers above are day-to-day actual in-use numbers.
Bizjets typically cruise in the .75-.80 bracket, just a bit faster than the average, and Cessna really likes to tout the big dick, er um, I mean high max cruise speed, of the Citation X. The airplane is even designed to look phallic. But it seems to work. CEOs love 'em.
Bizjets are also generally range limited, which means the extra range they get from flying well below their advertised max cruise is often critical to getting where they’re going without a time-wasting fuel stop. As a result, regardless of the advertised numbers, they’re often doing .78 like the rest of us.
An issue they, and we, encounter all the time is there is essentially a one-lane road to each major airport. You can’t go faster than the guy in front of you. There are routes from all over the place converging in towards any major city. As those get closer together, eventually you get one logical line of traffic even if we’re still on separate routes/altitudes.
And once they all get in a line, the slow poke sets the pace.
In theory with different altitudes available you could run at different speeds, at least for the enroute cruise portion of the flight. As a practical matter that doesn’t play out much with modern traffic density. Eventually everybody needs to fit through one spot in the sky with 10-15 miles between them. On crap weather days, the spacing increases to 30 miles, just to meter the flow into the airport down to a rate they can handle.
Imagine passing somebody on the freeway where he’s doing 60, your max speed is 62, and you can’t get back in his lane until you’re 2 miles ahead of him. That takes a lot of distance & time. Multiply eveything by 10 & you get an idea of what we’re dealing with. To pass somebody enroute from LA to NYC you’ve got to start over Illinios & finish over Ohio, because the one-lane off ramps are in central Pennsylvania.
Years ago (like the late 80s), bizjets could fly higher than the typical 727 / MD80 / early 737 and often had better navigation tools. So they could get above the airliners and drive directly to the other end of their route, while the airliners zig-zagged their way from one radio navigation beacon to another. The zigs are small, maybe a 10 degree course change every ~200 miles. But over a long haul that ads up to a few extra minutes.
Now everybody has direct here-to-there navigation with INS + GPS. And the current airliners run high enough that there is only a little space above them for the bizjets “express lane”. So pretty much, they get in line with the rest of us, particularly in the eastern half of the US.
Bottom line: as others have said, 98% of the gain is on the ground, not in the air.