Is there a best practice for transporting a Torah scroll from one building, or one city, to another?
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.