In theory if you leap from the bus such that you are completely in the air for a moment, you won't be in contact with a conductor and the ground at the same time. (Given enough voltage, electricity can cross the gap to the ground, but if there's a fire you gotta do what you gotta do.) You then have to keep hopping with your feet together or shuffle-step away due the the potential energy difference in the ground.

A problem is that many people who use a bus are not physically capable of a leap. They may be elderly, disabled, pregnant or simply be very small children.

We learned as kids stay put unless absolutely having to leave the vehicle. If you had to leave because of say a fire you were to keep both feet together and literally hop away like you say not walk. This is going way back it seems to make sense but I haven’t checked the source on this.

Could thick rubber mats or blankets help? (or other non-conductive material) like an escape slide?

I've read that if you must, to hop with your feet together if you are near a downed line.

This video describes some of the hazards and how to avoid them. https://www.youtube.com/watch?v=fLVzvMTgGDY&t=170s

Would running work? (By running I mean literally jumping from one foot to the other).