I was on a train recently, and the child in the seat in front was sitting with her aunt (the mother was sitting with the baby further up the carriage). The aunt started listening to her iPod and reading a book. Nothing for child to do - aged 3 or 4.
I started passing objects through the gap between the seats, and she started passing them back. When that palled, I passed over a sheet of stickers and a colouring book with a couple of pencils. The aunt looked really surprised. the child coloured and stuck happily for about 20 minutes. I couldn't understand why child was expected just to sit quietly for a long journey.
In such a situation, I often wouldn't make any contact with the adult at all, just invite the child to join in with our play, or offer little objects which are age appropriate, if I have any. I can't bear the way people expect their children to go into neutral in those in-betweeny times on buses and trains.
For myself, and for any children travelling with me, I always have activities in my bag. If I am taking children for several hours in a constricted public space, it is my responsibility to make that a pleasant experience for my own family and for us not to make everyone around us unhappy, as far as possible.
What about the mothers who try to stop their bored children kicking off their shoes or making finger drawings on misted windows? I usually try to exchange conspiratorial glances with the beleagured child - I hate the way that all adults are assumed to be part of the adult conspiracy by default. But I find it very difficult to find cheerful liberating things to say to the mother - mostly leading by example, I guess, in trying to keep travelling children occupied and happy with whatever objects are available. I love seeing a family on one of those 4-seater tables on a train with all their books and colouring and games and snacks spread across the surface, obviously settled in all the way to Glasgow.