You can either turn them off completely in the game options after you have chosen your map. Or if you want to play with them on, just make sure that when the timer for the next raid hits zero you put bounty on another empire and make sure that when the raid is launched you have less bounty on you head than the other guy.

Here is what I do.

When timer hits zero I put 250 credits of bounty on another empire. I stay in the bounty screen until the raid has launched, because if that race puts money on my head that causes me to have a greater amount than the other guy I instantly up him by 250 I repeat this until the raid has been launched

Visual representation.

Starting bounties of head Me: 0 Other Guy: 0

1. Timer hits zero. Me=0 Other Guy= 250

2. bounty is placed on my head. Me=500 Other Guy=250

3. I up him by 250 immediatly. Me 500 Other Guy= 750

4. Repeat process if necessary, Raid launches, Pirates go after Other Guy.

This process has never failed for me.

No problem, I can't garuntee this will work but as I said, it never fails for me. When I play a 1v1 this tactic is essential for me. When I'm playing larger maps with more AI, the AI will place bounty among themselves often so I don't have to worry about the bounty on my head as much.