Hi Amie and welcome to FPN! I also have this issue with the paper from this company. While there are some people who have never had issues with Moleskines, I find that I can only write on one side of the paper and, at that, it does bleed through. I have therefore stopped writing in Moleskine journals. I believe the finer the nib, the less bleeding will occur. Also, the less saturated inks might be a good bet. Diamine and J.Herbin don't bleed as much as the Private Reserve or Noodlers.
There have been many discussions on this very topic and they are probably in the paper forum. I know that may not be a help to you but I always rely on some generous person to post links to the exact discussion because I rarely have the time (or success) when faced with doing a search!
I hope this helps but in any event, welcome!