Well, 100 km/hr is a 15 day journey, if you're talking several hundred km/hr, then you're cutting that down to five days.
Which is, admittedly, a heck of a lot slower than I imagined it would be, but the supposition is that for stability sake, they're starting to think maximum speed would be about 60 km/hr, which would mean the 36,000km journey would take 25 days.
However, humans tend to go to low earth orbit - the space station's at 350km from the earth - 60km/hr to there would only take about six hours, a far more practical situation, though still one heck of an interesting onramp since all the rest of the traffic is going 27000km/hr faster than you are.
Yes, admittedly, you'd still have to transfer from the Beanstalk (which, like a very tall tower, is effectively motionless relative to the Earth's surface) to the untethered space station whizzing by (at about 8 km per sec) in low Earth orbit.
People currently "tend" (a curious choice of words on your part) to go to LEO not because there's anything intrinsically interesting there, but rather only because it's the nearest/lowest/cheapest "spot" which is nonetheless already in "true" space.
I, personally, have no problem with a long, stately "drive" into geostationary orbit. Who's in a hurry?
Regards,