Is there a best practice for transporting a Torah scroll from one building, or one city, to another?
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There is alot on this topic. Some say 10 people should accompany the Torah. Also it is customary to cover it with a tallis. The Torah should not pass by dirty areas. For more of a comprehensive idea see here.
I would summarize the procedure as "treat the Sefer Torah with honour". At least two people accompanying the Sefer, covered as as far as possible, don't go anywhere dirty or unpleasant. I had to take a Sefer for correction when I was a student. There were two of us, we took the train and then a taxi (students didn't have cars then). Obviously if it is raining there is the need to protect the Sefer from damage as well. A large plastic bag would come in handy but then there should be another cover (cloth, tallit etc.) as an honourable covering.