Enslaving girls, torturing girls, and kidnapping girls for non-payment (let him go and have your men follow him home) will raise the suspicion level, so are to be avoided.
What I have found to work the best for non-payment is to either take his daughter (if that option is available) or to send him to my dungeon, then torture and release, all in the same turn.
Following those guidelines, I am bribing at 100 gold per week, have a "Benevolent" reputation, and a suspicion level of "Town Scum" with no raids.