If heads have turned purple, they are cut off and placed in bags. Once heads are purple, the seeds continue to develop. If not bagged, these seeds would mature and blow free. Some would germinate, spreading the plants. Dead plants can be left on site, but any purple flower heads must be removed in bags and burned.
Prevention is the most cost effective approach.
After any type of ground disturbance, quickly seed with desirable species to minimize the opportunity for bull thistle to become established. If in other parks, contact the Superintendent. Tell them about the location of the plants so they can be mapped for future work projects. Do not remove plants without permission in writing or direction from a private land owner, manager or, if on public lands, an agency official.