With 1000 dollars each, it seems that bribing with bitcoin would be a good idea. One USB stick will do the job with no third party required.
Bribing itself is a bad idea.
But if you still want to bribe,then bitcoin would be much easier to bribe than using cash.Since there is no bank transaction involved here,it could not be traced.Just a click will do sending bitcoins from your wallet to the other address.
Bitcoin is a very easy money to be used for bribe work. And that was certainly made by so many people. And I think that's a bad idea for bad guys. I feel hated and do not want it to happen. It is a criminal offense and affects everyone, and it affects the reputation and the cleanliness of bitcoins. I hate it.
I dont think that bribing someone with bitcoin will increase your chance of success.
It is harder to make a transaction quick, you need to have some kind of mobile access to send the bitcoin.
I can spot another problem in this idea, because not every law enforcement officer will use
BTC as a way to hold/save money, so the plan will be ruined if someone will not be interested in cryptocurrencies.
As naughty1 already said, the bad guys can make their way easier by bribing police with cash, instead of offering them to make a transfer with BTC.