Before answering this question, think about this: Have you ever seen the Moon whiz across your line of sight like a meteor? The answer of course, is no. Even though the Moon is traveling around the Earth at over 2,000 miles (3,200 km) per hour, at its average distance of 239,000 miles (382,000 km) from Earth, its orbital motion is barely perceptible.
The Moon seems to creep roughly its own diameter eastward against the star background. Similarly, although a bright naked comet might be moving at many tens of thousands of miles/kilometers per hour through the inner solar system, its overall distance from Earth likely will measure in tens of millions of miles/kilometers.
So while a bright comet will indeed appear to move, because of its distance from Earth, its apparent night-to-night movement against the background stars is very slow. So it moves across the sky in the fashion of the Moon (or the planets for that matter), not in the fashion of a streaking meteor.