Hello @Paul Kraemer
No matter what the .bat file runs in it will still require permissions to the folder to copy files. You will need to give the user write access to the folder or they will not be able to copy files.
A work around solution is that you could have her write to a proxy folder (with write access) and schedule a xcopy command to be ran on the server that moves the files from the proxy folder to the folder that she has read-only access to.
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If this is helpful please mark as correct answer.