The approach maneuvers required several days.
The hard part is not maintained by the Hubble , once you’ve put your hand because both objects are artificial satellites orbiting our planet.
The hard part is to get in that orbit when you go to the Earth . Imagine you have to find a parking spot that moves in a certain area of the city to more than 20,000 kilometers per hour. Your car can reach those speeds, but has shot out of the land surface in another direction, and also you’ll crash into the orbit.
Possibly, without a proper calculation of the path, passing thousands of miles away from your target. Indeed, the complicated maneuvers of approaching Space Telescope took several days to get an orbit similar first, and then go slowly approaching.
When your speed is similar to the Hubble , then you will not notice that tens of thousands of km / h.