Yes and no.

The first part of the skill, "Deal # Dmg to an adjacent unit with a Bleed Effect Die on it" works like any standard damaged based attack or skill. Both Thick Skin and Hardy will be considered when accounting for this damage.

The second part of the skill, "Unit takes 1 True Dmg for each position it moves" specifically uses True Dmg, which will work around Think Skin. As Hardy mentions accounting for True Dmg in its description, it will still only lose 1 HP even if it moves twice on its turn.