If Stellacorn is bounced back from being stunned going to a battlefield, do I draw from movement?

No, you do not draw a card in that scenario.

According to the rules and established rulings for Riftbound:

1. Recall vs. Move: A "Recall" (the mechanic that moves a unit back to the base after it is stunned or fails to conquer) is distinct from a "Move" action. As defined in Rule 450 and confirmed in RiftJudge FAQ #9617 and FAQ #10024, a recall is not a move.
2. Trigger Condition: Your Stellacorn Herder's ability ("When I move, draw 1") specifically triggers only upon a Move action. Because the unit is being recalled to the base, the trigger condition is never met.

As clarified in RiftJudge FAQ #9481, which addresses a similar interaction with recall effects, the game distinguishes strictly between these two actions; therefore, any ability triggered by a "move" will not fire when a unit is recalled.