Student or Learner
I understand "run it" is "to say" but what does "by" mean here?
M:Can we talk about you inviting your friends over?
W: I'm sorry, I didn't think you'd mind
M: I also live here, so I'd like to have a say in what goes on.
W:OK, I'll be sure to run it by you next time..
To run something by (or past) someone means to let them know your plans in advance to see if they have any objections (or perhaps input).
Before you propose that idea to Steve, run it by Ruth first to see if she has any input. She's worked with Steve a bit in the past and might have some insight.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.