Who is responsible for travel expenses if my ex moved out of town and did not file a sheer in court

Who pays for travel expenses will be an issue for the court to decide.  A parent is supposed to file a notice of relocation, so that these issues can be dealt with smoothly.  I presume you have an existing court order for custody and parenting time, and if that order does not address the issue, then you should go back to court to have the judge deal with these new circumstances.  Good luck!