The ISS is in orbit about 250 miles high, the students in this related question get 62 miles in less than a minute. This NASA Press release indicates the The Soyuz TMA-13M launch on May 2014 has a 6 hour trip duration.
At 65 miles per hour I can drive 250 miles in less than 4 hours. Is it really a 6 hour trip by rocket? If so why?
Docking is a slow process. The Space Shuttle rendezvous timeline took 6 hours from start to finish. With 4½ hours to go, the Shuttle was 250,000 feet (76 km) behind the Space Station. With 3 hours to go, the Shuttle was about 50,000 feet (15 km) behind. Relative velocities became slower as the Shuttle closed in on the Station. The last 400 feet were incredibly slow, taking about 40 minutes.
That's typical. Docking is slow. The Soyuz expedited docking is rather bold. Approach and rendezvous is typically measured in days, not hours.
Update
Why is docking such a slow process? The answer is safety, errors (faults), uncertainties, and reaching the target (phasing). I'll deal with these in reverse order.
Achieving the Space Station's orbit is easy. Just do a Hohmann transfer and be done with it. That's not nearly good enough when it comes to rendezvous. The target vehicle has to reach a specific point on the Space Station's orbit at a specific time to dock or berth with it. Having spare time helps. A vehicle could make the Hohmann transfer from the insertion orbit to the Station orbit immediately after launch, but that means zero tolerance for uncertainties, errors, and safety. An easy solution for dealing with reaching the target: Take your time.
There are lots of uncertainties in launching a vehicle into space. The vehicle might well be placed in orbit, but not the planned one. Having a 20 km uncertainty in altitude an even bigger uncertainty in along-track is typical. That launch uncertainty was one of the key reasons TMA-12M had to use the standard slow approach rather than the planned fast track approach. Uncertainties pop up all over the place. An easy solution to dealing with these uncertainties: Take your time.
There's a big difference between uncertainties and errors. Uncertainties are what confound the vehicle when everything is behaving according to spec. Errors are what confound the vehicle when things don't behave according to spec. A thruster might provide 97% of nominal thrust one time, 102% the next. That's uncertainty. When the thruster is commanded off and a valve breaks so it stays off, permanently: That's a fault. That failed valve doesn't manifest itself as an error until the next time the control system commands the thruster on. The thruster remains off, just as expected, up until that "thruster on" command.
Rendezvous has to be fault tolerant. In fact, it has to be two failure safe for unmanned vehicles coming to the Station, and two failure tolerant for manned vehicles. The difference between the two: An unmanned SpaceX that goes reeling off into space because it suffered two failures is a loss, but a manageable loss, so long as it doesn't crash into the Station. A manned vehicle that goes reeling off into space because it suffered two failures is not a manageable loss.
Dealing with those failures takes time. Ensuring that a vehicle that has sustained two failures will not collide mandates a gradual phasing (which takes time) and a very, very slow final approach (which takes a lot of time). The Station safety rules dictate a rather cautious approach to rendezvous.
