A survey of plant-based wastes identified sunflower ( Helianthus annuus ) bark extract (SBE), produced via twin-screw extrusion, as a potential biostimulant. The addition of SBE to Arabidopsis ( Arabidopsis thaliana ) seedlings cultured in vitro showed a dose-dependent response, with high concentrations causing severe growth inhibition. However, when priming seeds with SBE, a small but significant increase in leaf area was observed at a dose of 0.5 g of lyophilized powder per liter. This optimal concentration of SBE in the culturing medium alleviated the growth inhibition caused by 100 mM NaCl. The recovery in shoot growth was accompanied by a pronounced increase in photosynthetic pigment levels and a stabilization of osmotic homeostasis. SBE-primed leaf discs also showed a similar protective effect. SBE mitigated salt stress by reducing the production of reactive oxygen species (ROS) (e.g., hydrogen peroxide) by about 30% and developing more expanded true leaves. This reduction in ROS levels was due to the presence of antioxidative agents in SBE and by activating ROS-eliminating enzymes. Polyphenols, carbohydrates, proteins, and other bioactive compounds detected in SBE may have contributed to the cellular redox homeostasis in salt-stressed plants, thus promoting early leaf development by relieving shoot apical meristem arrest. Sunflower stalks from which SBE is prepared can therefore potentially be valorized as a source to produce biostimulants for improving salt stress tolerance in crops.