it was a good 8 hours between the second bumps, usually when a thread is inactive for 8 hours, it USUALLY stays that way
there is no rule against bumping, however there is a rule against abusing the pm system,
it says "In addition, Private Messages are not intended to deprive the Community of valuable information or experiences which could benefit the entire group. Please do not use private messages if the content of the message can be helpful to others"
therefor, you should have the debate here and explain why he shouldn't bump threads instead of pming him