Actually, running can help prevent varicose veins by building the calf pump muscle which improves circulation and blood return.
If there are bulging varicose veins symptoms like swelling, heaviness, pain and leg fatigue may make it difficult to run. Should you still want to run consider the following:
Avoid running on hard surfaces
Wear compression bandage while running
If your varicose veins are bad, bulging and symptomatic then avoid running but you could continue walking, swimming and other low impact physical activity.