Hi there
I followed the guide above, and it didn't seem to work - not sure if it's been in a patch since the last solution, but I'm fairly certain that time in the apartment no longer counts towards the bounty timer:
I got an AI bounty on a populated server, ran for my life for about 20 minutes with several close shaves (Turns out if you get run over by a jet, you 'die' as oppose to 'get killed by...' so that doesn't count as losing your bounty), and eventually made it back to my apartment where I let it idle for about 3 hours irl. Achievement didn't pop, so I left if to idle for another few irl hours. Still nothing, so I switched to an invite only lobby, and it popped after 1 and a half minutes.
To get to the invite only lobby, do: Start menue -> single player -> Online -> Join GTA online (Should give you some options after this) -> Start invite only session, and then let it idle OUTSIDE OF YOUR APARTMENT AND GARAGE
Hope this helps

BWV 538