To rank up in cop career you collect Bounty and you pretty much just need to play the game naturally. You will get to rank 20 around the same time you get your last Distinction (or gold medal in Racer career).
In case you want to artificially boost via certain actions, these are your options:
- Damaging a player vehicle
- Performing a Takedown
- Busting a racer
- Gaining racer lead positions
- Performing close calls
- Drifting
- Reaching the top speed of a vehicle
- Evading EMPs, Helicopters, Spike Strips or Roadblocks
- Successfully activating Turbo with no collisions
- Taking shortcuts
- Driving in the oncoming lane
- Completing events
- First position - 8,000 to 12,000 bounty
- Second position - 5,000 to 7,000 bounty
- Third position - 1,000 to 4,500 bounty
- Beating Autolog recommendations
I am a pretty bad racing games gamer and took me around 16 hours to finish the COP career to lvl 20 and all distinctions.
Hope this helps!!