About how far away does the comet Hale-Bopp travel away from the sun?

Right to the edge of our Solar System. That's 370 astronomical units (AU), or 370 times the distance from the Sun to the Earth.

Comet Hale-Bopp was discovered in 1995. It's the most travelled comet in our Solar System that we know of. It came close to the Sun in 1997 and will not return until about the year 4380.

The distance from the Sun to the dwarf planet Pluto is 39 AU which pales by comparison with the distances covered by this comet.

https://scaleofuniverse.com/en/universe/distance-from-comet-hale-bopp-to-sun