This is the route I've found to be most optimal in my Any% Cop runs, both for saving time and for being able to get more bounty to where we can minimize most of the bounty grinding to a minimum, (which is something you may end up having to do for Car 12).

Route for Tier 1:

• Priority Target
• Just Rampage
• Performance Review
• Highway 5-0
• Leadfoot Lawman
• Thin Blue Finish Line

Route for Tier 2:

• Aggression Check
• Law Of Acceleration
• Sole Suspect
• Doughnut Run
• Ill Legal
• Perp Herder

Route for Tier 3:

• Take Out The Trash
• Clock On
• Pedal Meddler
• Taking Liberties
• Martial Law
• Prosecution Unrest

Route for Tier 4:

• Time Cop
• Takedown Showdown
• Rogue Officers
• Blue Shift
• Extreme Prejudice (Only if you don't have enough bounty for Car 12) - Repeat Takedown Showdown until Car 12 is unlocked
• The Duel (Cop)

Notes:

• If you feel you're not consistent with getting 3 stars at Aggression Check, you can swap Aggression Check and Law Of Acceleration around, though if you can get 3 stars at Aggression Check a lot of the time, it's not worth it to do this.
• I'd highly recommended that everywhere except Tier 4, keep note of what stage in your current tier is fastest that you can easily get 3 stars on. The reason being if you manage to not have enough bounty to get another car in instances outside of Tier 4, you may be able to bring your run back by doing the fastest available stage for you in your current Tier.