Possible Clues:

• Stepped (across)
• Set off carrying a gun: was on foot
• Carrying a stick set off: was walking
• Walked fast with long steps
• Marched into bistro demanding instant service
• Took deliberate steps
• Walked around Dorset
• So the saint was riding? No, walking
• Went with a purpose
• A high-minded individual had transport but went on foot